A distributed cooperative optimal load-sharing control is proposed for one class coupled parallel-connected dynamical systems with non-identical nonlinear dynamics. The communication among subsystems is modeled as a digraph. The input-output linearization technique is adopted to transform the load-sharing control design into a tracking synchronization problem of a general linear multi-agent system. LQR-based method is introduced to design the cooperative optimal load-sharing control law with tunable gains based on the nearest neighbor principle, which makes the coupling strength only depend on the communication topology and the control gain only depend on the sub-system model. The asymptotically stability of the entire closed-loop systems can be decoupled into each sub-system's stability through matrix transformation. Assuming that the directed graph has a spanning tree, the stability of the whole system can be proved with the aid of the Lyapunov function. A desired response speed can be obtained by tuning the control parameters with the proposed method. Simulation results verify the effectiveness and feasibility of the proposed approach.