Reliability sensitivity determines the relationship between reliability and the distribution parameters of uncertain variables, and guides reliability analysis and reliability design. A novel non-probabilistic reliability sensitivity analysis method based on ellipsoidal convex model was presented, in which non-probabilistic reliability sensitivity was defined as a partial derivative of non-probabilistic reliability index with respect to the distribution parameters of uncertain variables. The analytical equations of non-probabilistic reliability sensitivity for linear limit state functions were first derived. Through-two different choices of the linearization point, the approximate functions of non-linear limit state functions can be then obtained by using the first-order Taylor expansion, then the approximate analytical equations of non-probabilistic reliability sensitivity were given. Several numerical examples will be used to demonstrate the effectiveness and feasibility of the proposed methods.