A novel distributed model predictive control algorithm for continuous-time nonlinear systems is proposed in this paper. Contraction theory is used to estimate the prediction error in the algorithm, leading to new feasibility and stability conditions. Compared to existing analysis based on Lipschitz continuity, the proposed approach gives a distributed model predictive control algorithm under less conservative conditions, allowing stronger couplings between subsystems and a larger sampling interval when the subsystems satisfy the specified contraction conditions. A numerical example is given to illustrate the effectiveness and advantage of the proposed approach.