Propagation and amplification of partial coherent light (PCL) is simulated with a 3-D propagation code and fast Fourier transformation. The PCL is useful to realize highly uniform irradiation on a target in internal confinement fusion. On the other hand, the PCL has speckle structure in space and time owing to partial coherence. The intensity modulation due to speckles is enhanced by self-focusing in laser glasses due to nonlinear refractive index. Calculations on the laser propagation for the PCL show that the speckles of cm scale self-focus to 10 mm scale. As a result, average fluence of the PCL is limited at lower level comparing with that of the coherent laser. Experimental results are also coincident with the simulation results.