We present an novel algorithm that reconstructs voxels of a general 3D specular surface from multiple images of a calibrated camera. A calibrated scene (i.e. points whose 3D coordinates are known) is reflected by the unknown specular surface onto the image plane of the camera. For every viewpoint, surface normals are associated to the voxels traversed by each projection ray formed by the reflection of a scene point. A decision process then discards voxels whose associated surface normals are not consistent with one another. The output of the algorithm is a collection of voxels and surface normals in 3D space, whose quality and size depend on user-set thresholds. The method has been tested on synthetic and real images. Visual and quantified experimental results are presented.