Scalability and Complexity are crucial performance parameters in the design of Interconnection networks for multiprocessor system. This paper proposed and analyzed a new scalable interconnection network topology named as Linear Crossed Cube (LCQ). LCQ designed is based on the principle of hypercube architecture however, it improves some of the drawbacks of hypercube such as complex extensibility and its VLSI Layout. It inherits most of the desirable properties of hypercube type architectures; the most notably are small diameter and symmetry. LCQ has linear extension at each level of the extension while preserving all the desired topological properties. To evaluate the performance of proposed LCQ, standard scheduling algorithms are being implemented on it. The performance parameters such as Load Imbalance Factor (LIF) and balancing time are evaluated on the proposed LCQ as well as on other similar multiprocessor architectures. To compare the performance of proposed LCQ, standard scheduling scheme is also implemented on other similar multiprocessor architectures. The comparative simulation study shows that the proposed network can be considered as low-cost multiprocessor architecture for parallel system when appropriate scheduling algorithm is implemented onto it.