Heterogeneity of resources can not be ignored while scheduling application task graphs in grid environment. In this paper, a list-based task scheduling algorithm, called scheduling with heterogeneity using critical path (SHCP) for grid computing system is presented. Some other scheduling algorithms such as HEFT use mean execution time based b-level for deciding task priority and ignore the importance of critical path. In SHCP, a critical path based task sequence is generated where variance based computation and communication costs are used. The experimental results show that SHCP algorithm performs better than HEFT and HHS algorithms in grid environment for large task graphs and at high CCRs.