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One stochastic process that is often used to model real phenomena is the compound Poisson process (CPP). CPP is a process in which a component in the process of the events occurred is assumed to be a Poisson process with a certain intensity function (homogenous or nonhomogeneous). Thinning process algorithm is usually used to generate events that occurred in the Poisson process. The study aims to find out the algorithm for generating the CPP which has nonhomogeneous Poisson process (NHPP) intensity functions. The value of the load caused by the Poisson process is assumed to be a family of i.i.d random variables and the variables are also independent of the Poisson process. The results of this study have obtained the thinning process algorithm and its generalizations for compound Poisson process having nonhomogeneous Poisson process (NHPP) intensity functions. This algorithm is the result of developing theory and computational simulation analysis by generating data that can be applied in various fields of science.