This paper presents a branch-current distribution system state estimation algorithm considering zero-injection constraints. The algorithm takes the branch-current amplitude and phase angle as state variables, considering current-amplitude measurement easily without measurements conversion and makes full use of voltage amplitude measurements, power measurements and current measurements. In order to improve the robust performance of algorithm, exponential function is adopted as the objective function in this paper. The paper takes simulation test to verify the algorithm correctly and effectively on improved IEEE 34 nodes system.