In this paper, an extension of Precision Time Protocol (PTP) to enable energy-efficient clock synchronization between the nodes within Wireless Sensor Network (WSN) is proposed. PTP is nanosecond accuracy clock synchronization protocol in which nodes are organized in master-slave hierarchy on the basis of clock accuracy by means of Best Master Clock (BMC) algorithm. The algorithm considers clock accuracy to select best clock in the system. A novel modification of IEEE 1588 BMC algorithm for energy-constraint multi-hop WSN has been proposed to reduce clock convergence time and energy needed by considering out-degree of clocks without sacrificing synchronization accuracy. The new algorithm results in energy efficient clock synchronization that makes it most appropriate for low-power multi-hop wireless sensor networks. We present NS-3 simulation data that confirms the effectiveness of work. © 2018 IEEE.