Auto-focusing is a key technology in digital instruments and computer vision. In the focusing procedure, the focusing accuracy and anti-noise capability is crucial. Evaluation functions which based on high-frequency components have many advantages, such as sensitivity and focusing accuracy. They are suitable for the real-time system,however, they are easily corrupted by noise. Therefore, a new focusing evaluation function with good anti-noise capability has been proposed. Firstly,the proposed function abstracts high-frequency components through wavelet multi-resolution analysis (MRA). Some neighbor correlation exists in each sub-band coefficients,but noise is random, so the noise coefficients have no such correlation. The new function introduces a frequency sub-band threshold, supposing that the component value below than the threshold is noise, then filter it. In this way, noise and image signal could in general be separated. Experiments have proved that the proposed function has a sharp single apex as well as high sensitivity. Furthermore, it is significantly advanced in the anti-noise capability.