Task scheduling in cloud computing plays an essential role for service provider to enhance its quality of service. Grasshopper Optimization Algorithm (GOA) is an evolutionary computation technique developed by emulating the swarming behavior of grasshoppers while searching for food. GOA is easy to implement but it cannot make full utilization of every iteration, and there is a risk of falling into the local optimal. This paper proposes a suitable approach for adjusting the comfort zone parameter based on the fuzzy signatures called signature GOA (SGOA) to balance exploration and exploitation. Then, we propose task scheduling based on SGOA by considering different objectives such as completion time, delay, and the load balancing on the machines. Finally, different algorithms such as Particle Swarm Optimization (PSO), Simulated Annealing (SA), Tabu Search (TS), and multi-objective genetic algorithm, are used for comparison. The results show that among all algorithms, SGOA can be successful in much less iteration.