Hydraulic model of water distribution systems (WDSs) is an essential tool to realize modernization management of WDSs. To make the model capable of reflecting the system's behavior with reasonable accuracy and achieving intended purposes, the parameters in it should be calibrated. The nodal demand calibration of WDS models is formulated as a nonlinear optimization problem, which is then solved iteratively using weighted least squares method. Comparing to previous studies, the proposed method deduces the analytical solution of Jacobian matrix of WDSs based on matrix analysis method, and translates the under-determined problem to over-determined by aggregating the nodal demand using demand allocation matrix, such that the computational efficiency and the reliability of calibration results were improved. A simple network is used to illustrate the computation of Jacobian matrix, the construction of gradient vectors and the aggregation of nodal demand. The practicability of the method is further validated by a real network.