For the problem that task scheduling program in cloud computing environments usually takes high response time and communication costs, a Honey Bee Behavior inspired Load Balancing (HBB-LB) algorithm was proposed. Firstly, the load was balanced across Virtual Machines (VMs) for maximizing the throughput. Then the priorities of tasks on the machines were balanced. Finally, HBB-LB algorithm was used to improve the overall throughput of processing, and priority based balancing focused on reducing the wait time of tasks on a queue of the VM. The experiments were carried out in cloud computing environments simulated by CloudSim. The experiment results showed that HBB-LB algorithm respectively reduced average response time by 5%, 13%, 17%, 67% and 37% compared with Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Dynamic Load Balancing (DLB), First In First Out (FIFO) and Weighted Round Robin (WRR) algorithms, and reduced maximum completion time by 20%, 23%, 18%, 55% and 46%. The result indicates that HBB-LB algorithm is suitable for cloud computing system and helpful to balancing non-preemptive independent tasks.