A simple weighted-density approximation based on both local average and bulk densities is proposed. The weighting function is constructed to agree with that of the hybrid weighted-density approximation (HWDA) proposed by Leidl and Wagner [J. Chem. Phys. 98, 4142 (1993)] for the homogeneous fluid; it has the advantage of being simpler to apply. The new approximation is applied to predict the homogeneous and inhomogeneous properties of classical fluids. For the homogeneous classical fluids, the new approximation generates the same accurate higher-order direct correlation functions as those of the HWDA. For the properties of inhomogeneous classical fluids such as the density profiles of hard-sphere and Lennard-Jones fluids restricted in spherical cages, the results are in good agreement with the computer simulations, and comparable with those of the HWDA. Through these calculations, the density-functional perturbation theory based on the second-order perturbation theory of the uniform liquid has also been examined.