In this paper, a surjective mapping that satisfies the Li–Yorke chaos in the unit area is constructed and a perturbation algorithm (disturbing its parameters and inputs through another high-dimensional chaos) is proposed to enhance the randomness of the constructed chaotic system and expand its key space. An algorithm for the composition of two systems (combining sequence based on quantum random walks with chaotic system’s outputs) is designed to improve the distribution of the system outputs and a compound chaotic system is ultimately obtained. The new compound chaotic system is evaluated using some test methods such as time series complexity, autocorrelation and distribution of output frequency. The test results showed that the new system has complex dynamic behavior such as high randomicity, unpredictability and uniform output distribution. Then, a new scheme for generating pseudorandom numbers is presented utilizing the composite chaotic system. The proposed pseudorandom number generator (PRNG) is evaluated using a series test suites such as NIST sp 800-22 soft and other tools or methods. The results of tests are promising, as the proposed PRNG passed all these tests. Thus, the proposed PRNG can be used in the information security field.