Embodiments for performing surface rendering upon volume data in an ultrasound system are disclosed. An ultrasound data acquisition unit transmits and receives ultrasound signals to and from a target object to thereby acquire ultrasound data corresponding to a plurality of frames. A volume data forming unit forms volumes data corresponding to the plurality of frames based on the ultrasound data. The volume data includes a plurality of voxels. A processing unit detects edges of a region of interest (ROI) of the target object in the volume data and performs surface rendering upon voxels within the detected edges to thereby form a 3-dimensional ultrasound image.