A three-dimensional weighted cone beam filtered backprojection (CB-FBP) algorithm (namely 3D weighted CB-FBP algorithm) has been proposed to reconstruct images from the projection data acquired along a helical trajectory in angular ranges up to [0, 2π]. However, an over scan is usually employed in the clinic to provide premium image qualities for an accurate diagnosis at the most challenging anatomic structures, such as head, spine and extremities. In an over scan, the corresponding normalized helical pitch is usually smaller than 1:1, under which the projection data acquired along angular range larger than [0, 2π] can be utilized to reconstruct an image. To improve noise characteristics or dose efficiency in an over scan, we extended the 3D weighted CB-FBP algorithm to handle helical pitches that are smaller than 1:1, while the algorithm's other advantages, such as reconstruction accuracy and computational efficiency, are maintained. The novelty of the extended 3D weighted CB-FBP algorithm is the decomposition of an over scan with an angular range corresponding to [0, 2π + Δβ] (0 < Δβ < 2π) into a union of full scans with an angular range corresponding to [0, 2π]. As a result, the extended 3D weighted function is a weighted sum of all 3D weighting functions corresponding to each overlapped full scan. An experimental evaluation shows that, the extended 3D weighted CB-FBP algorithm can significantly improve noise characteristics or dose efficiency of the 3D weighted CB-FBP algorithm at helical pitch smaller than 1:1, while its reconstruction accuracy and computational efficiency are maintained. It is imortant to indicate that, the extended 3D weighting function is still applied on projection data before 3D backporjection, resulting in the computational efficiency of the extended 3D weighted CB-FBP algorithm comparable to that of the 3D weighted CB-FBP algorithm. It is believed that, such an efficient CB reconstruction algorithm that can provide premium image qualities at low helical pitches will find its extensive applications in CT medical imaging.