In this paper, a generalized form of chaotic map based on nonlinear function with parabolic shape is introduced. The study involves the investigation of chaotic dynamics in terms of apparent in time-domain, and both qualitatively and quantitatively examination using bifurcation diagram and Lyapunov exponents. Furthermore, the practical application of these parabolic chaotic maps is showcased in a pseudorandom number generator, with its performance evaluated using statistical tests from the NIST SP800-22 test suite.