Currently, cone-beam computerized tomography (CT) and micro-CT scanners are under rapid development for major biomedical applications. Half-scan cone-beam image reconstruction algorithms assume only part of a scanning turn, and are advantageous in terms of temporal resolution and image artifacts. While the existing half-scan cone-beam algorithms are in the Feldkamp framework, we have published a half-scan algorithm in the Grangeat framework for a circular trajectory [Med. Phys. 30, 689-700 (2003)]. In this paper, we extend our previous work to a helical case without data truncation. We modify the Grangeat's formula for utilization and estimation of Radon data. Specifically, we categorize each characteristic point in the Radon space into singly, doubly, triply sampled, and shadow regions, respectively. A smooth weighting strategy is designed to compensate for data redundancy and inconsistency. In the helical half-scan case, the concepts of projected trajectories and transition points on meridian planes are introduced to guide the design of weighting functions. Then, the shadow region is recovered via linear interpolation after smooth weighting. The Shepp-Logan phantom is used to verify the correctness of the formulation, and demonstrate the merits of the Grangeat-type half-scan algorithm. Our Grangeat-type helical half-scan algorithm is not only valuable for quantitative and/or dynamic biomedical applications of CT and micro-CT, but also serves as an intermediate step towards solving the long object problem.