Massive wireless connections are emerging in Internet of Things (IoT) and will lead to a severe spectrum scarcity issue. To deal with this issue, we introduce the cognitive radio technology into the IoT, namely, cognitive IoT. Different from a conventional cognitive network, the cognitive IoT is dominated by short-packet transmissions, which suffer from a significant packet error rate even when the transmission rate is smaller than the Shannon capacity. In this paper, we jointly optimize the spectrum sensing time and packet error rate to maximize the cognitive effective-throughput, which is defined as the effective transmission rate by considering the packet error rate. First, we formulate an instantaneous effective-throughput maximization problem with the instantaneous channel state information (CSI) between cognitive transceivers, and develop a successive optimization algorithm. Second, we formulate an average effective-throughput maximization problem with the statistical CSI between cognitive transceivers. Due to the complicated expression of the average effective-throughput, we analyze its closed-form expression and adopt an exhaustive search method to obtain the optimal solution. Numerical and simulation results reveal that, the packet length has a significant impact on the optimal design. Meanwhile, the proposed algorithms can almost maximize the instantaneous/average effective-throughput.