Based on the time-dependent theory, the emission property of two-dimensional anisotropic random laser under femtosecond laser pumping is theoretically investigated by using a Gaussian function to describe the pumping process. The temporal properties of the random laser emission including the peak intensity, delay time and pulse width, are traced with the variation of the sample size, surface filling-fraction and radius of the scatterer. The results show that the behavior of random lasing depends strongly on the system parameters, one can control the output waveshape through modify the above three parameters. The present work can offer more theoretical guidance for the application of the anisotropic random laser, especially the controllability of output waveshape.