Heat exchanger network (HEN) and utility system are both important compositions in chemical industry. Heat exchanger network contributes to recover heat from process streams and sometimes consumes external heat resources when heat demand is not satisfied by itself. Rankine cycle-based utility system supplies steams to motivate processes if external heat is needed, meanwhile produces power in turbine. Thus, there is great necessity to synthesize HEN and utility system simultaneously. In this work, a stage-wise HEN superstructure model considering the optimal placement of heaters and matches of streams is presented to integrate with utility system, wherein heaters that consume utility steams are allowed to be placed inside each stage and also between adjacent stages. The selection and allocation of the steams in different pressure levels are optimized considering both power generation in utility system and heat recovery in HEN. A mixed-integer nonlinear programming (MINLP) formulation is formulated for the optimal design of HEN-utility system with minimum total annualized cost (TAC), aiming at trade-off amongst capital cost, fuel cost and income of selling power. At last, a case is studied to demonstrate the application of the proposed method, obtaining a desired HEN configuration with meaningful economic benefits.