With the rapid development of technology, “A robot in every home” will come true in the near future. Path planning for mobile robots, as an important object of robotics, has drawn amount of attentions. Inspired by the strict hierarchy and division of responsibilities by social group of animals, social group search algorithm is proposed in this paper. Individuals are classified into four groups with different search strategies according to leader-follower model. When the individuals are searching for optimal object, head leader is the best candidate and searching for better position along with leaders, which are the subordinates with well performance. Followers find the proper position by following the leaders and searching better one around them. Meantime, dispersed numbers are the also-runs which perform the worst and should be replaced by new-borns. Leaders and followers are responsible for searching optimal position, while dispersed numbers ensure the algorithm beyond the local optimum. Furthermore, crossover and mutation, as well as elimination mechanisms are introduced to our algorithm to enlarge the search scope. As a result, comparing with genetic algorithm and particle swarm optimizer, the possibility of premature and local optimum is reduced. The convergence is verified mathematically and experimentally. Via numerous simulations and comparison with other classical algorithms, the characters of high efficiency and effectiveness for path planning problem are illustrated, which are especially of great significance for the further research in robotic navigation.