With the advancement of technology, multi-cores with shared cache have been used in real-time applications. In such systems, some cores run real-time applications and some cores run other non-critical applications that do not have strict deadline. Due to the sharing of cache by multi-core processors, problems predicting the actual execution time and the execution time of real-time applications have emerged. To address these problems, cache memory with prioritized replacement policy is proposed. Most of the work is carried out in high-level hardware designs and software based application level designs. No low-level hardware implementations of cache memory with prioritized replacement circuits have been designed to the best of my knowledge. My thesis focuses on designing a LRU replacement circuit that is prioritized based on the application the processor is running. Real-time applications acquire priority in using the cache memory over other applications which enhance the seamless execution of the real-time application and hence supports execution time predictability which in turn helps improve the potential of multi-core computing of real-time systems. The speed, size and power overhead are analyzed by placing the N-way set associative LRU as a part of cache of size 128KB designed using 65nm CMOS technology.