This paper addresses the problem of quantized feedback control of nonlinear Markov jump systems (MJSs). The nonlinear plant is represented by a class of fuzzy MJSs with time-varying delay based on a Takagi-Sugeno fuzzy model. The quantized signal is utilized for control purpose and the sector bound approach is exploited to deal with quantization errors. By constructing a Lyapunov function which depends both on mode information and fuzzy basis functions, the reciprocally convex approach is used to derive the criterion which is able to ensure the stochastic stability with a predefined l2-l∞ performance of the resulting closed-loop system. The design of the quantized feedback controller is then converted to a convex optimization problem, which can be handled through the linear matrix inequality technique. Finally, a simulation example is presented to verify the effectiveness and practicability of the proposed new design techniques.