Task scheduling and resource allocation are important problems in grid computing. The workflow management system receives inter-dependent tasks from the users and allocates each task to an appropriate resource based on user requirements and constraints such as budget and deadline. Thus this system has a significant effect on performance and the efficient use of resources. In general, mapping tasks to distributed resources is an NP-hard problem. Hence, heuristic and meta-heuristic methods are typically employed. Moreover, since tasks can enter the system at any time, the task scheduling runtime is an important parameter for workflow management systems. This paper presents a fast method for scheduling workflows in a grid environment based on a multi-objective Genetic Algorithm (GA). In the proposed method, the workflows and chromosomes in the GA are assigned to levels to reduce the scheduling time. In addition, the proposed method prevents infeasible solutions being produced in new generations, so task dependencies do not need to be checked. New crossover and mutation operators are proposed to improve convergence and maintain solution diversity. Experimental results are presented and evaluated using several well-known metrics as well as a new metric. This shows the effectiveness of the proposed method compared to other approaches.