To reconstruct the topology of a diffusion network, existing approaches customarily demand not only eventual infection statuses of nodes, but also the exact times when infections occur. In real-world settings, such as the spread of epidemics, tracing the exact infection times is often infeasible; even obtaining the eventual infection statuses of all nodes is a challenging task. In this work, we study topology reconstruction of a diffusion network with incomplete observations of the node infection statuses. To this end, we iteratively infer the network topology based on observed infection statuses and estimated values for unobserved infection statuses by investigating the correlation of node infections, and learn the most probable probabilities of the infection propagations among nodes w.r.t. current inferred topology, as well as the corresponding probability distribution of each unobserved infection status, which in turn helps update the estimate of unobserved data. Extensive experimental results on both synthetic and real-world networks verify the effectiveness and efficiency of our approach.