A new approach for robust H-infinity filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework.The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multi-objective optimization.The resulting H-infinity filter guarantees asymptotic stability of the estimation error dynamics with exponential convergence and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties.Explicit bounds on the nonlinear uncertainty are derived based on norm-wise and element-wise robustness analysis.