In this paper, a new distributed Kalman filter is proposed for state estimation of systems with acyclic digraph, namely acyclic systems. This method can be applied to a number of large-scale systems including sensor networks and formation flying missions. An acyclic system can be represented by an overlapping block-diagonal state space (OBDSS) model, which requires an extensive communication overhead for implementing a centralized Kalman filter scheme. The OBDSS model is transformed into our proposed constrained-state block-diagonal state space (CSBDSS) model, which is purely diagonal and simplifies the implementation of a distributed Kalman filter scheme. Corresponding to each Kalman filter iteration a specific constrained-state condition needs to be satisfied that is embedded with a fusion feedback. Simulation results confirm the effectiveness of our proposed analytical work.