Resource scheduling in the cloud computing is affected by multiple objectives. Usually, users hope that tasks can be completed as soon as possible while using the lowest cost of cloud resources. To address the trade-off between task completion timeliness and resource cost, meta-heuristic algorithms show significant optimization potential. As a new type of meta-heuristic algorithm, the Cuckoo Search algorithm features few parameters and an excellent random search path. But, it has deficiencies in local search ability and convergence speed. In this paper, an Simulated Annealing Multi-Objective Cuckoo Search algorithm (SAMOCS) is proposed, which aims to balance the completion time and resource cost. SAMOCS combines the non-dominated sorting and spatial crowding degree as the fitness comparison operator, and updates the solutions through a discarding probability based on simulated annealing. In this way, it improves the local search ability of the algorithm, reduces the task execution time, and at the same time lowers the resource cost of executing cloud tasks. According to the numerical simulation results of four commonly used multi-objective test instances, SAMOCS has better global convergence accuracy than the original multi-objective Cuckoo Search algorithm. Resource scheduling experiments on cloud computing with CloudSim platform show that the task completion time can be reduced by up to 11%, and the resource cost can be saved by up to 7% compared to the current mainstream resource scheduling algorithms.