The Mobile Sink based data collection in wireless sensor network can reduce energy consumption efficiently and has been a new data collection paradigm. In this paper, we focus on exploring polynomial algorithm to compute the constrained trajectory of the Mobile Sink for data collection. We first present a universal system model for designing constrained trajectory in large-scale wireless sensor networks and formulate the problem as the Maximizing Energy Reduction for Constrained Trajectory (MERC) problem. We show that the MERC problem is NP-hard and design an approximation algorithm (CTMER), which follows the greedy approach to design the movement trajectory of the Mobile Sink by maximizing the effective average energy reduction. Through both rigid theoretical analysis and extensive simulations, we demonstrate that our algorithm achieves high computation efficiency and is superior to other Mobile Sink based data collection methods in aspects of energy consumption and network lifetime.