This paper have investigated the dual polarization oscillations (DPO) and associated dynamical behaviors in laser-diode-pumped microchip Nd:GdVO4 laser. Some optical properties of Nd:YAG, Nd:YVO4, and Nd:GdVO4 laser materials are compared. The higher thermal conductivity of Nd:YAG makes it suitable for higher-power applications. The larger stimulated-emission coefficient of Nd:YVO4 material makes it favorable for increasing light-light conversion efficiency. However, Nd:GdVO4 material has high thermal conductivity and large stimulated-emission coefficient. Many experiments done to study Nd:GdVO4 crystal¡¦s properties focused on the efficiency of high power generation. Orthogonal linearly-polarized emissions could be obtained in fluorescence spectrum of Nd:GdVO4, but DPO did not be observed in Nd:GdVO4 laser possessing a large fluorescence anisotropy with laser-diode pumping. In this paper, DPO on different transitions in laser-diode-pumped microchip Nd:GdVO4 are obtained for the first time. Furthermore, more effective generation of dual polarization oscillations is affected by the pumping conditions associated with different temperature gradient than different pumping power density. The results imply that DPO can be generated without having to use additional optical elements and Nd:GdVO4 material is suitable for the construction of compact DPO lasers. Laser properties including oscillation spectra, input-output characteristics, pump-dependent pattern formations and noise power spectra are studied experimentally. A poor mode matching between the pump beam and lasing beam results in the generation of high order transverse modes. The observed anti-phase dynamics have been explained in terms of the reduced three-dimensional cross-saturation of population inversions among orthogonally-polarized modes. The study of dynamics of microchip Nd:GdVO4 lasers under pump modulation has also been reported in this paper. Different phase correlations among laser modes are obtained by tuning the modulation frequency and amplitude. The observed dynamical states are reproduced theoretically by rate equations of multimode class-B lasers including the cross-saturation among individual modes and the pump modulation.