In this paper, we propose a robust method to estimate the camera spectral sensitivity function using a neural-network-based model and a custom learning algorithm. A new and specially designed architecture for training our neural network model is presented to estimate the spectral sensitivity as a function of wavelength. The sensitivity function is modeled as the sum of a few Gaussian functions, and a radial basis function neural network is trained to approximate this function over the visual wavelengths. No constraints are imposed on the illumination distribution or spectral sensitivity, as similar methods usually do. Experimental results show that the proposed method produces superior results with much lower root mean square error compared to the methods using basis functions or constraint optimization approaches. Study of the reproduced colors also verifies the accuracy of our method.