In this paper a sliding-mode observer based on the equivalent control method for discontinuous functions for a class of non-linear systems is proposed. The observer structure and its existence conditions are presented. Besides, a class of high order sliding operators with the properties of uniform (w.r.t. initial conditions) finite time convergence and with reduction of chattering effect are exposed. The use of these operators in the observer design allows the calculation of the equivalent control and the observer convergence uniformly in finite time. A simulation example is presented to illustrate the proposed method.