Recently, Low Earth Orbit (LEO) satellite-based Internet of Things (LEO-IoT) becomes attractive for computation offloading in mobile-edge computing (MEC) since it can overcome terrain obstacles, such as in depopulated villages and disaster sites. However, it is extremely hard to allocate bandwidth and power resources jointly with multiple users and satellites. In this paper, we study offloading in collaborative LEO-IoT where satellites forward data from users to the MEC server, with the goal of making offloading fast and energy efficient. To achieve this goal, we first define the data offloading in collaborative LEO-IoT as an optimization problem with resource constraints. Then we formulate the optimization problem as a Partially Observable Markov Decision Processes (POMDP), which differs from the existing Markov Decision Processes (MDP) work for the offloading scenario. We further propose a novel Multi-Agent Information Broadcasting and Judging (MAIBJ) algorithm to allocate resources in a collaborative manner. Finally, extensive experiments are conducted with various configurations and the results show that MAIBJ can shorten at least 33% of transmission latency and save at least 42% of energy consumption compared with several baseline algorithms.