Physics-informed radial basis networks (PIRBNs) were found to be more effective than physics-informed neural networks (PINNs) in solving nonlinear partial differential equations (PDEs) with high-gradient features and sharp solutions. Inspired by adaptive finite element methods and incremental learning ideas, a radial basis network based on residual/gradient Gaussian adaptive sampling (G-PIRBN) was proposed to further improve the approximation accuracy of the model in fitting the high-gradient regions of nonlinear PDEs. During the training process, a Gaussian mixture distribution was generated using the current residual and gradient information, which was utilized for subsequent specific Gaussian distribution sampling. The newly added sampling points were trained together with historical data to accelerate the convergence of network loss and achieve higher fitting accuracy. Experimental results of point-wise absolute error, mean square error, and average time consumption for nonlinear spring equations, wave equations, and diffusion equations demonstrated that G-PIRBN exhibited higher fitting accuracy and faster fitting speed than PINN, PIRBN, and EI-Grad when solving nonlinear PDEs with high-gradient characteristics.