Utilizing mobile sensors to locate chemical gas sources in the air can be applied to security searches, disaster relief, and building environments. This study investigates the problem of gas source localization using mobile robots in indoor environments and proposes a time-weighted maximum likelihood estimation algorithm (TWMLE). Based on a sampling time-weighting mechanism, the algorithm utilizes the observation samples that contain gas concentration, wind speed, direction, and its relative localization to iteratively estimate and approach the position of local plume source, accommodating the time-varying gas distributions and airflows in dynamic turbulent environments. Meanwhile, this study employs a local sensing window to constrain the feasible solution space of the estimated source location to ensure the feasibility of the estimation results, achieving short-term estimation of local plumes in unknown environments and effectively enhancing estimation stability. Additionally, this study weights average the multiple estimation results based on the gas detection condition, effectively enhancing the ability to search upwind when gas is detected and the ability to quickly rediscover the plume when gas is missed. The experiments are implemented to evaluate the proposed method in four indoor environments with different airflow conditions and obstacles, as well as in a real environment. The proposed TWMLE algorithm outperforms both the infotaxis algorithm and the surge-cast algorithm in terms of success rate and search performance. In the real environment, the success rate of the TWMLE algorithm reaches 90.0%, which is higher than the 80.0% of the infotaxis algorithm and the 60.0% of the surge-cast algorithm. The results show that the proposed TWMLE algorithm can effectively locate the gas source in complex indoor environments.