This paper proposes a distributed collaborative complete coverage path planning (CCPP) algorithm based on a heuristic method to solve a CCPP problem for multiple agents in an unknown environment. Based on the relationship between path length, energy consumption and number of turns, the algorithm instructs the agents to autonomously plan their respective paths in real time by giving the priority of directions. Simulation experiments show that the proposed CCPP algorithm can guarantee efficient collision-free complete coverage compared with related approaches.