The energy efficient problem of parallel-connected pumps in heating, ventilation, and air-conditioning (HVAC) systems has received an increasing attention in recent years. While many pump optimization methods are proposed and show great performance, pumps are not always energy efficient and lack flexibility. In this paper, we propose a distributed control algorithm for parallel pumps in HVAC system in a peer-to-peer setting. Based on a spanning tree of the network of the intelligent nodes and a population of potential solutions randomly sampled, the algorithm makes optimal control decision for pumps to minimize energy consumption and meet the system demand. The theoretical analysis on convergence of the algorithm is established. Unlike traditional control structure, the whole system is fully distributed and each pump is controlled by an intelligent node that runs identical control code and coordinates with other nodes through direct data exchange. Simulation experiments on 6 parallel-connected pumps are provided for different working cases to demonstrate the effectiveness of the proposed algorithm and compare with other four methods. The results show that our method strictly satisfies the demand constraint and presents a good energy saving potential, the convergence guarantee, the flexibility. The maximum energy saving can be up to 29.92%. Besides, the hardware test clearly presents that our method can perform on low-cost Raspberry Pi3 and reduce system cost.