In this paper, we consider the uniform parallel machine scheduling problem with release dates and job rejection. In this problem, given a set of jobs to be arranged subject to the job release dates, each job is either accepted to process on one of $m$ uniform parallel machines or rejected by paying its rejection penalty. The goal is to minimize the sum of the makespan of accepted jobs and the total rejection penalty of rejected jobs. When $m$ is a fixed constant, we provide a pseudo-polynomial time dynamic programming exact algorithm. When $m$ is arbitrary, we derive an approximation algorithm. If the number of accepted jobs is no less than $(m-1)$, then the derived approximation algorithm achieves the performance ratio of 3; otherwise, the derived approximation algorithm achieves the performance ratio of $(2+\rho)$, where $\rho$ is the ratio of the maximum machine processing speed to the minimum machine processing speed. In the end, by a numerical experiment, we illustrate the running way for the derived approximation algorithm.