Abstract　 　 
Various astrophysical phenomena such as gamma-ray bursts(GRBs), super Nova explosion, and relativistic jet from active galactic nuclei show synchrotron radiation, which indicate strong magnetic fields and particle acceleration. Both of these important physical processes, strong magnetic field generation and particle acceleration, may be explained by the Weibel instability. I will discuss our particle simulation studies on the relativistic Weibel instability, showing an excellent agreement with the linear theory in the early growth phase of the instability and a qualitative agreement with the quasilinear prediction in the later phase.