Leaky Wang kWTA is introduced. As compared with the original Wang kWTA, its state equation consists of a leaky term on the right hand side which leads to the differential equation with right hand side discontinuous and there is no equilibrium point in classical sense. By the theory of discontinuous dynamic systems, the dynamics of the leaky Wang kWTA is formulated as a Filippov differential inclusion and its state convergence is proved. Moreover, the state dynamics is in essence a gradient system which minimizes a non-smooth convex energy function and its exact convergence time is derived. Let \(u_{\pi _1} < \cdots < u_{\pi _n}\) be the inputs. The state converges to \(u_{\pi _{n-k}}\) irrespective to its initial condition. In the presence of input noise, the state converge to a value close to \(u_{\pi _{n-k}}\) . Finally, the effect of state leak on the Wang kWTA with Heaviside function is discussed and methods for solving such effect are investigated.