Dual-wavelength pulse lasers have a wide range of applications in terahertz wave generation, Doppler radar coherence detection, spectral studies and so on, so how to generate dual-wavelength pulse lasers is of great significance. Dual-wavelength pulse lasers can be realized by Q-switched technology, which can be divided into active Q-switching and passive Q-switching. Compared with the active Q-switched lasers, the passive Q-switched lasers have the advantages of simple technology and small size. In order to obtain a stable dual-wavelength pulsed laser, one approach is pumping two crystals or combinatorial crystals into a cavity, another approach is pumping a single crystal into a cavity. Compared with the dual-crystal laser, the single-crystal laser has the advantages of simple structure, convenient operation, and easier miniaturization. But there is gain competition between two wavelengths of single crystal laser, so it is difficult to output two-wavelength pulse laser. In this paper, a 1 063 nm/1 065 nm dual-wavelength pulsed laser using a single Nd∶GdVO₄ crystal and a single Cr⁴⁺∶YAG crystal is proposed.The Q-switched process of laser can be described by rate equation. By establishing a simulation model based on rate equation, the influence of pump power on the time-domain characteristics of laser output under different reflectivity of output mirror is studied. The theoretical results show that when the reflectivity of the output mirror is changed, the threshold inversion particle number density of the two wavelengths will change accordingly. Therefore, the dual-wavelength pulsed laser can be realized by changing the reflectivity of the output mirror. When the π-polarized output mirror reflectivity is in the range of [0.52,0.71] and σ-polarized output mirror reflectivity is 0.95, the laser can output dual-wavelength passively Q-switched pulse. By increasing the pump power, π-polarized single-wavelength pulse, dual-wavelength multiple-on-one pulse, dual-wavelength one-on-one pulse, dual-wavelength one-on-multiple pulse and σ-polarized single-wavelength pulse can be generated in sequence.In order to verify the influence of pump power on time characteristics of dual-wavelength pulse, a Y-type-cavity dual-wavelength laser is designed. The reflectivity of π-polarized output mirror is set to 0.60, and that of σ-polarized output mirror is set to 0.95. The stimulated emission cross section of Nd∶GdVO₄ crystal is kept constant by setting the cooling temperature of the temperature controller at 20 ℃. The output of the Nd∶GdVO₄ laser is coupled to two channels of the oscilloscope by two identical photodetectors. The pulse waveform of the Nd∶GdVO₄ laser at different pump power is measured by changing the pump source. With the increase of the pump power, the pulse laser with the time mentioned above characteristics is output in turn, which is consistent with the numerical simulation results. When the pump power is 5.51 W, the output of the laser is a one-on-one pulse of two orthogonal polarized wavelengths, of which the π and σ polarized wavelengths are 1 063.23 nm and 1 065.52 nm respectively, the average power is 323 mW and 462 mW respectively, and the peak pulse power is 11.62 W and 20.35 W respectively, the pulse repetition rate is 141 kHz.In this paper, by setting up the rate equation model of two-wavelength quadrature polarization passively Q-switched laser based on Nd∶GdVO₄ crystal, the condition of laser output dual-wavelength pulse and the influence of pump power on the time characteristics of laser output under different reflectivity of output mirror are studied. The simulation results show that the dual-wavelength pulse can be realized by adjusting the reflectivity of the output mirror to change the double-wavelength threshold inversion of the particle number density. On the premise of realizing dual-wavelength pulse output, the output pulse waveform can be changed by changing the pump rate. The experimental results are in good agreement with the simulation results under the condition of 20 ℃.