A new soft-fault diagnosis approach for analog circuits with parameter tolerance is proposed in this paper. The approach uses the fuzzy nonlinear programming (FNLP) concept to diagnose an analog circuit under test quantitatively. Node-voltage incremental equations, as constraints of FNLP equation, are built based on the sensitivity analysis. Through evaluating the parameters deviations from the solution of the FNLP equation, it enables us to state whether the actual parameters are within tolerance ranges or some components are faulty. Examples illustrate the proposed approach and show its effectiveness.