This paper focuses on network coding based multirate multimedia streaming in directed networks and aims at maximizing the total layers received by all receivers, which directly determine the quality of video streaming. We consider the property of layered coding in video streaming and propose the Layer Separated Network Coding Scheme (LSNC) for layered video streaming. Two algorithms OLSNC and SLSNC are proposed for LSNC based video streaming, where OLSNC achieves an optimal solution, while SLSNC is a polynomial time approximation algorithm. Simulation results show that LSNC is an efficient network coding scheme for multirate multimedia streaming, and the aggregated number of received layers of both OLSNC and SLSNC is very close to the theoretical upper bound in all configurations analyzed.