The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) was launched on 15 September 2018 to measure ice sheet and glacier elevation change, land elevation, global vegetation elevation and monitor clouds and aerosols. The sole instrument on-board ICESat-2 is the Advanced Topographic Laser Altimeter System (ATLAS). ATLAS employs a micro-pules multi-beam photon-counting laser lidar technology, which is the first time this technology has been applied to a spaceborne platform. However, since the laser pulses emitted and detected by ATLAS are weak signals, the ICESat-2 data introduces a significant number of noise photons. The denoising of the ICESat-2 data is a key point for its application.A few algorithms have been proposed to remove noise photons in the ICESat-2 data, which are based on the criterion that signal photons are more densely distributed than noise photons. Most of the denoising methods nowadays depend on the set parameters and the parameter-free method is becoming a new frontier. To fix the current parameter-free quadtree denoising method which misidentifies noise photons under the strong noise background, this paper proposes an improved parameter-free denoising method for the ICESat-2 point cloud. For avoiding the noise photons sparse in density but close in the distance in a partial area, which means photons may be separated by the original quadtree and misrepresented as a high density, the pruned quadtree is used to represent a suitable density. According to the location of ICESat-2 photons, the initial space is given and recursively divided into four quadrants. Instead of dividing until each quadrant contains no more than one photon, a quadrant is not divided in the case that the quadrant is divided once and its internal photons are not separated. The density of photon is the corresponding level value in the tree structure. Then, several equidistant windows are divided according to the along track distance to adapt the changes of SNR. The Otsu method adaptively calculates the photon density threshold of each window. Photons with level values less than the density threshold are removed to complete the first-level denoising. After that, there may be a small number of outlier noise photons with a high local density and cannot be identified by the pruned quadtree, the box-plot is used to complete the second-level denoising. Considering that the change of elevation will affect the box-plot denoising, equidistant windows are also divided according to the along track distance. Photons whose elevations in each window are not within the upper and lower thresholds calculated by box-plot are identified as noise photons.Using the data from North Dakota and California to carry out the denoising experiments for the ICESat-2 point cloud under strong noise. The airborne lidar elevation products with a resolution of 1m are used as the verification data, and the denoising effect is verified by a combination of qualitative and quantitative methods. Experimental results show that: 1) Compared with the original quadtree denoising method, the number of noise photons misidentified by the pruned quadtree method is reduced under strong noise. Based on the advantages of pruned quadtree, the proposed pruned quadtree method combined with box-plot is also superior to the quadtree method combined with box-plot in terms of denoising effect; 2) The ground and canopy top curves fitted by the signal photons obtained by the quadtree method have large deviations from the profile elevation curves of the airborne lidar elevation products, while the curves fitted by the signal photons obtained by the proposed method can basically be consistent with the profile elevation curves. Moreover, the accuracy evaluation results of the proposed method are better than those of the quadtree method. The $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ and $R^{\mathrm{2}}$ values of the ground accuracy evaluation corresponding to the proposed method in study area 1 are 0.91 m and 0.997, respectively. The $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ and $R^{\mathrm{2}}$ values of the ground accuracy evaluation corresponding to quadtree method in study area 1 are 10.51 m and 0.713, respectively. In study area 2, the $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ values of the ground and canopy top accuracy evaluation corresponding to the proposed method are 2.47 m and 3.56 m with the $R^{\mathrm{2}}$ values are 0.999 and 0.998, respectively. The $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ corresponding to quadtree method are 90.92 m and 90.17 m with $R^{\mathrm{2}}$ are 0.156 and 0.400. Overall, the proposed method without input parameters is effective for removing noise photons in the ICESat-2 data under strong noise.