One of the most important aspects of a set of color image sensors is to capture colorimetric information about an object being imaged. The estimation accuracy of the colorimetric information depends not only on the spectral sensitivities of the sensors but also on the noise present in the color image acquisition device. In this paper, for the technical tractability, the problem on the design of an optimal set of spectral sensitivities with Gaussian distribution functions is addressed based on a colorimetric evaluation model. It is shown that the shapes of the optimal spectral sensitivities change to linearly independent sensitivity curves with a decrease in signal-to-noise ratio (SNR) to suppress the noise effects and that optimization must be done at a specific noise level of a device.