An improved slime mold algorithm (IMSMA) is presented in this paper for a multiprocessor multitask fair scheduling problem, which aims to reduce the average processing time. An initial population strategy based on Bernoulli mapping reverse learning is proposed for the slime mold algorithm. A Cauchy mutation strategy is employed to escape local optima, and the boundary-check mechanism of the slime mold swarm is optimized. The boundary conditions of the slime mold population are transformed into nonlinear, dynamically changing boundaries. This adjustment strengthens the slime mold algorithm’s global search capabilities in early iterations and strengthens its local search capability in later iterations, which accelerates the algorithm’s convergence speed. Two unimodal and two multimodal test functions from the CEC2019 benchmark are chosen for comparative experiments. The experiment results show the algorithm’s robust convergence and its capacity to escape local optima. The improved slime mold algorithm is applied to the multiprocessor fair scheduling problem to reduce the average execution time on each processor. Numerical experiments showed that the IMSMA performs better than other algorithms in terms of precision and convergence effectiveness.