A post processing-based Software Receiver is implemented in MATLAB for the Indian Regional Navigation Satellite System (IRNSS), also called as NavIC (Navigation with Indian Constellation). IRNSS is developed by Indian Space Research Organization (ISRO). It provides navigation related services over India and its neighbouring countries and comes into operational status with the seven satellites in the desired orbits. This NavICSR (NavIC Software receiver) is useful for further research and development of the IRNSS/NavIC system. NavIC research community can analyse the NavIC signals, to carry out ionospheric studies and to develop new algorithms. NavICSR is capable of processing the Digital ADC data of IF signals stored in the files for L5 and S band signals and provides the navigation solution to the users. It is configured to run for all quantization levels, sampling rates and real or IQ input IF data, up to the position fix. This is developed by modifying and adding the required algorithms to the existing Open-source GPS SDR for L1 C/A signals developed by Dennis M. Akos et al. The existing post-processing receiver’s frame work is replaced with the developed time synchronous frame work in NavICSR, which aims to get real time execution speed in MATLAB on a standard normal PC. In the developed frame work, all the assigned tracking channels will process the data simultaneously in a time synchronous manner. Tracking channels work on one millisecond data and compute the receiver position for every millisecond then process the data of next millisecond. In the developed frame work the input IF data is processed continuously with a circular buffer and updates the navigation solution continuously. This paper mainly emphasises the modifications needed in GPS Software receiver to adopt to IRNSS and presents the position accuracies obtained with both signals at L5/S bands. Acquisition, Tracking and data decoding algorithms of NavICSR are briefly explained. Time synchronous frame work is analysed in this paper for the real time capability of the receiver with minimum sampling frequency, bandwidth and number of satellites in view. The preliminary results are shown in terms of Time to first fix (TTFF) and speed of execution. The experiments are carried out with the IRNSS IF data stored in a file with the real signals obtained from the IRNSS front-end. The Results shows that NavICSR is flexible and reconfigurable enough for prototyping and a base for further research and development. The speed to run this software receiver is half of the real time speed. i.e. it will take double time as compared to real time. It can be further improved easily for real time speeds by optimizing all modules individually, such as acquisition, tracking, data decoding, computation of pseudoranges, position of satellites and receiver using proposed framework.