Conventional interpolation algorithms for reconstructing freehand three-dimensional (3D) ultrasound data always contain speckle noises and artifacts. This paper describes a new algorithm for reconstructing regular voxel arrays with reduced speckles and preserved edges. To study speckle statistics properties including mean and variance in sequential B-mode images in 3D space, experiments were conducted on an ultrasound resolution phantom and real human tissues. In the volume reconstruction, the homogeneity of the neighborhood for each voxel was evaluated according to the local variance/mean of neighboring pixels. If a voxel was locating in a homogeneous region, its neighboring pixels were averaged as the interpolation output. Otherwise, the size of the voxel neighborhood was contracted and the ratio was re-calculated. If its neighborhood was deemed as an inhomogeneous region, the voxel value was calculated using an adaptive Gaussian distance weighted method with respect to the local statistics. A novel method was proposed to reconstruct volume data set with economical usage of memory. Preliminary results obtained from the phantom and a subject's forearm demonstrated that the proposed algorithm was able to well suppress speckles and preserve edges in 3D images. We expect that this study can provide a useful imaging tool for clinical applications using 3D ultrasound.