Due to the strong anti-destructive ability, global coverage, and independent infrastructure of the space-based Internet of Things (S-IoT), it is one of the most important ways to achieve a real interconnection of all things. In S-IoT, a single satellite can often achieve thousands of kilometers of coverage and needs to provide data transmission services for massive ground nodes. However, satellite bandwidth is usually low and the uplink and downlink bandwidth is extremely asymmetric. Therefore, exact data collection is not affordable for S-IoT. In this paper, an approximate data collection algorithm is proposed for S-IoT; that is, the sampling-reconstruction (SR) algorithm. Since the uplink bandwidth is very limited, the SR algorithm samples only the sensory data of some nodes and then reconstructs the unacquired data based on the spatiotemporal correlation between the sensory data. In order to obtain higher data collection precision under a certain data collection ratio, the SR algorithm optimizes the sampling node selection by leveraging the curvature characteristics of the sensory data in time and space dimensions. Moreover, the SR algorithm innovatively applies spatiotemporal compressive sensing (ST-CS) technology to accurately reconstruct unacquired sensory data by making full use of the spatiotemporal correlation between the sensory data. We used a real-weather data set to evaluate the performance of the SR algorithm and compared it with two existing representative approximate data collection algorithms. The experimental results show that the SR algorithm is well-suited for S-IoT and can achieve efficient data collection under the condition that the uplink bandwidth is extremely limited.