After proposing the carbon peaking and carbon neutrality target, China further proposed a series of specific carbon emission growth limit sub-targets. How to decarbonize the energy system to ensure the realization of the carbon growth limit sub-targets is a meaningful topic. At present, generation expansion planning of renewable energy in integrated energy systems has been well studied. However, few of the existing studies consider specific carbon emission growth targets. To address this research gap, a two-stage robust generation expansion planning framework for regional integrated energy systems with carbon growth constraints is proposed in this paper, which takes into account multiple uncertainties. In this framework, the objective function is to minimize the total operation cost and wind turbine investment cost. The first stage is the decision-making level of the wind turbine capacity configuration scheme. The second stage is the optimal economic dispatching in the worst-case scenario, which is a bi-level problem of max-min form. Thus, the two-stage robust optimization framework constitutes a problem of min-max-min form, which is pretty hard to solve directly with a commercial solver. Therefore, a nested column-and-constraint generation algorithm is adopted and nested iterations are performed to solve the complex problem. Finally, case studies are carried out on a regional electric-gas integrated energy system. The MATLAB/YALMIP simulation platform with the Gurobi solver is used to verify the effectiveness and superiority of the proposed framework. Compared with other four cases, 5,000 Monte Carlo scheduling tests demonstrate that the proposed framework can ensure the system carbon emission to be controlled within a certain limit even in the worst scenario. Due to the consideration of multiple uncertainties, the proposed framework planning results are both robust and economical for investment. This study can provide theoretical support for the actual regional integrated energy system to achieve a certain carbon growth target.