Manycast routing and spectrum assignment (RSA) in elastic optical networks (EONs) has become a hot research field. In this paper, the mathematical model and high efficient algorithm to solve this challenging problem in EONs is investigated. First, a multi-objective optimization model, which minimizes network power consumption, the total occupied spectrum, and the maximum index of used frequency spectrum, is established. To handle this multi-objective optimization model, we integrate these three objectives into one by using a weighted sum strategy. To make the population distributed on the search domain uniformly, a uniform design method was developed. Based on this, an improved grey wolf optimization method (IGWO), which was inspired by PSO (Particle Swarm Optimization, PSO) and DE (Differential Evolution, DE), is proposed to solve the maximum model efficiently. To demonstrate high performance of the designed algorithm, a series of experiments are conducted using several different experimental scenes. Experimental results indicate that the proposed algorithm can obtain better results than the compared algorithm.