This paper developed the dynamic feedback neural network model to solve the convex nonlinear programming problem proposed by Leung et al. and introduced subgradient-based dynamic feedback neural networks to solve non-differentiable convex optimization problems. For unconstrained non-differentiable convex optimization problem, on the assumption that the objective function is convex coercive, we proved that with arbitrarily given initial value, the trajectory of the feedback neural network constructed by a projection subgradient converges to an asymptotically stable equilibrium point which is also an optimal solution of the primal unconstrained problem. For constrained non-differentiable convex optimization problem, on the assumption that the objective function is convex coercive and the constraint functions are convex also, the energy functions sequence and corresponding dynamic feedback subneural network models based on a projection subgradient are successively constructed respectively, the convergence theorem is then obtained and the stopping condition is given. Furthermore, the effective algorithms are designed and some simulation experiments are illustrated.