This paper proposes a new scheduler applying the concept of non-uniform laxity to Earliest deadline first (EDF) approach for aperiodic tasks. This scheduler improves task utilisation (Execution time / deadline) and also increases the number of tasks that are being scheduled. Laxity is a measure of the spare time permitted for the task before it misses its deadline, and is computed using the expression (deadline - (current time + execution time)). Weight decides the priority of the task and is defined by the expression (quantum slice time / allocated time)*total core time for the task. Quantum slice time is the time actually used, allocated time is the time allocated by the scheduler, and total core time is the time actually reserved by the core for execution of one quantum of the task. Non-uniform laxity enables scheduling of tasks that have higher priority before the normal execution of other tasks and is computed by multiplying the weight of the task with its laxity. The algorithm presented in the paper has been simulated on Cheddar, a real time scheduling tool and also on SESC, an architectural simulator for multicore platforms, for upto 5000 random task sets, and upto 5000 cores. This scheduler improves task utilisation by 35% and the number of tasks being scheduled by 36%, compared to conventional EDF.