The overall performance of Multi-Processor System-on-Chip (MPSoC) platforms depends highly on the efficient communication among their cores in the Network-on-Chip (NoC). Routing algorithms are responsible for the on-chip communication and traffic distribution through the network. Hence, designing efficient and high-performance routing algorithms is of significant importance. In this paper, a deadlock-free and highly adaptive path-based routing method is proposed without using virtual channels. This method strives to exploit the maximum number of minimal paths between any source and destination pair. The simulation results in terms of performance and power consumption demonstrate that the proposed method significantly outperforms the other adaptive and non-adaptive schemes. This efficiency is achieved by reducing the number of hotspots and smoothly distributing the traffic across the network.