Internet of Things (IoT) is a promising paradigm to provide massive wireless connections in the future communications. One main feature of IoT is short packet communication (SPC), which adopts finite block-length codewords for data transmissions. Different from the long packet transmission (i.e., infinite block-length codewords) in conventional wireless networks, SPC suffers from a significant packet error rate even when the transmission rate is smaller than the Shannon capacity. To enhance the transmission efficiency as well as the reception reliability, we introduce cooperative relaying to the IoT network and propose a cooperative IoT protocol. Then, we analyze the average throughput of the cooperative IoT protocol with an approximated closed-form expression. Based on the closed-form expression, we design both optimal and suboptimal transmission rates to maximize the average throughput. Numerical and simulation results have validated the correctness of the theoretical analysis, and show that the maximum average throughput with the optimal/suboptimal design almost overlaps with the simulation results. Besides, we compare the proposed protocol with the automatic repeat request (ARQ) mechanism in terms of both the optimal transmission rate and the maximum average throughput, and observe that the proposed protocol outperforms the ARQ mechanism, especially for a medium/large number of cooperative users.