This paper presents an algorithm, called Earliest Deadline Critical Laxity (EDCL), for the efficient scheduling of sporadic real-time tasks on multiprocessors systems. EDCL is a derivative of the Earliest Deadline Zero Laxity (EDZL) algorithm in that the priority of a job reaching certain laxity is imperiously promoted to the top, but it differs in that the occurrence of priority promotion is confined to at the release time or the completion time of a job. This modification enables EDCL to bound the number of scheduler invocations and to relax the implementation complexity of scheduler, while the schedulability is still competitive with EDZL. The schedulability test of EDCL is designed through theoretical analysis. In addition, an error in the traditional schedulability test of EDZL is corrected. Simulation studies demonstrate the effectiveness of EDCL in terms of guaranteed schedulability and exhaustive schedulability by comparing with traditional efficient scheduling algorithms.