More than 130 countries and regions have put forward various climate goals, which makes carbon-oriented energy system planning a heated topic. However, these planning studies do not consider the carbon fixation role played by forest carbon sinks (FCSs). To take advantage of the carbon fixation role of FCSs, this paper will develop a carbon-cycle integrated energy hub (CC-EH) model to quantify the economic advantages of FCSs in planning a zero-carbon energy system, where energy flow and carbon flow are both analyzed. A total planning and operating costs minimization with the constraints of CO2 emissions is proposed as a mixed integer nonlinear programming (MINLP) optimization model and the overall problem is solved based on commercial solver. The proposed model is validated by case studies on six medium to large-size cities in different geographical locations in China. Results indicate that the typical cities in China can fulfill their carbon-neutral commitments by 2060. Throughout the entire planning period, FCSs can offset up to 55.31 % of the total carbon dioxide emissions from urban energy systems. Besides, FCSs achieved by forestation will help the energy system to reduce up to 36 % of the planning cost compared to the case without using FCSs.