This paper describes a computationally efficient numerical model for unsteady flow computations in open channel networks using the four-point Preissmann implicit scheme. The proposed algorithm achieves improved convergence and computational efficiency by: (1) adopting a junction point water stage prediction and correction technique based on recurrence coefficients in the double sweep algorithm for the Preissmann scheme; (2) incorporating an adaptive relaxation technique in the iterative loop; and (3) adopting a subtiming framework for time stepping. Subtiming strategy requires small computational time steps for only those channels of the network where temporal variations in flow conditions are significant, while larger time steps are taken in other channels. The subtiming strategy minimizes computational inefficiency due to temporal overdiscretization associated with schemes using uniform time step size throughout the domain. The application of the proposed algorithm is illustrated for three test cases. For a large network of channels, the proposed algorithm increased the computational efficiency by a factor of two, as compared to the conventional junction point water stage prediction and correction algorithm presently available in literature. © 2020 American Society of Civil Engineers.