The interaction between light and plasma is one of the key problems in an inertial confinement fusion system. Some instability processes will occur when the energy of laser is absorbed by plasma. Because reducing the coherence of laser can significantly restrain the instability of the plasma, in practice, a continuous phase plate (CPP) is often used to generate the speckle and thereby to restrain the nonlinear effect in plasma. To clarify the working mechanism of CPP, the propagation characteristics of speckle field are studied in this paper. Since there are two different kinds of media in the light path, the statistical optics theory and the matrix optics method are combined to analyze the propagation characteristics of the speckle field in plasma. The ABCD matrix of the plasma is deduced. And then intensity distribution properties of the speckle filed in the plasma are calculated. Meanwhile, the autocorrelation length of the speckle field is calculated and the mechanism of the nonlinear restraint is explained. The results show that the speckle field is a paseudorandom field. It will bring a random phase disturbance to the wavefront in the propagation direction. It is very different form the ordinary Gaussian beam, the speckle filed has a limited longitudinal autocorrelation length. Though the propagation rule of the speckle field in plasma is similar to that in air, when the laser transmits into plasma, the coherence of the laser speckle weakens rapidly. The autocorrelation length of the speckle field in the plasma is shorter than that in air. Therefore, many kinds of nonlinear effects can be restrained when the speckle transmits into plasma. Specially, the autocorrelation length of the speckle is much shorter in the high density plasma. So the result of suppressing the nonlinear effect is better in plasma with high density than that with low density. This characteristic is very helpful in restraining the different nonlinear effects in plasma.