The propagstion and transformation of pulsed Gaussian beams through paraxial optical systems are treated in 4-dimension spatial-temporal domain by using a 6×6 matrix.The optical system could be nonsymmetric, dispersive and time-varying. A generalized Huygens diffraction integral for pulsed beam is written in terms of blocks of transfer matrix. To characterize a nonsymmetric pulsed Gaussian beam a 3×3 complex curvature tensor,Q-1,is introduced. The transformation laws of Q-1 are derived. As an example, a grating-pair pulse compression system is analysed.