Modern embedded systems are being modeled as Heterogeneous Reconfigurable Computing Systems (HRCS) where Reconfigurable Hardware i.e. Field Programmable Gate Array (FPGA) and soft core processors acts as computing elements. So, an efficient task distribution methodology is essential for obtaining high performance in modern embedded systems. In this paper, we present a novel methodology for task distribution called Minimum Laxity First (MLF) algorithm that takes the advantage of runtime reconfiguration of FPGA in order to effectively utilize the available resources. The MLF algorithm is a list based dynamic scheduling algorithm that uses attributes of tasks as well computing resources as cost function to distribute the tasks of an application to HRCS. In this paper, an on chip HRCS computing platform is configured on Virtex 5 FPGA using Xilinx EDK. The real time applications JPEG, OFDM transmitters are represented as task graph and then the task are distributed, statically as well dynamically, to the platform HRCS in order to evaluate the performance of the designed task distribution model. Finally, the performance of MLF algorithm is compared with existing static scheduling algorithms. The comparison shows that the MLF algorithm outperforms in terms of efficient utilization of resources on chip and also speedup an application execution.