For computed tomography (CT) with a displaced detector array, projections should be weighted by a weighting function to fit the filtered-backprojection (FBP) image reconstruction algorithm. Existing weighting functions have complicated piecewise forms and do not give good noise suppression. This study uses Sigmoid-like exponential weighting function, which is continuous, differentiable, and simple. Fourier transforms are used for the weighted FBP algorithm to obtain the residual terms of the frequency response for white noise. The residuals of this function are lower than those of wary function at high frequencies. The fan-beam and cone-beam geometries with displaced detector arrays were simulated with the images reconstructed using the FBP weighted by the Parker function, Wang function, and the present function. Subjective and objective evaluations show that for ideal noise-free conditions, the image qualities for the three functions are quite close; while with noisy conditions, the images given by the present function are smoother with sharper edges and higher contrast with improved F-norm, and mean squared error (MSE), contrast noise ratio (CNR) indices. Thus, this function is simpler and gives better noise suppression than the existing Parker and Wang functions.