Grid computing has continued to gain applicability in various spheres of computing while multicore computers are also becoming ubiquitous. Most grid scheduling algorithms remain sequential while several attempts at parallelizing grid scheduling rely on the underlying hardware. To leverage the grid to meet the growing global computing need, a method to increase the efficiency of grid scheduling on parallel systems is required. This work aims at enhancing the parallel scheduling of Grid jobs on a duocore system. An arbitrary method was employed to group machines, a summation of the total processing power of machines in each group was computed. Then, a size (of jobs) proportional to processing power (of machines) was used to allocate jobs to machine groups. The MinMin scheduling algorithm was implemented in parallel (multi-scheduling) within the groups and also implemented without the group method to schedule the same range of jobs on a single processor machine and on a duocore machine. A performance improvement of 16%, 49%, and 71% was recorded on the duocore system by the group method over the ordinary MinMin method using two, four, and eight groups respectively. We find that the group method increased the performance of the scheduling algorithm on duocre systems. Secondly, we find that the ordinary MinMin algorithm benefited from the underlying parallelism of the duocore but not as much as the group method. Thirdly, we find that performance of the scheduling algorithm increases as the number of groups increases. We conclude that job grouping and multi-scheduling enhance performance significantly on the ducore system.