Purpose: To develop a novel, fast converging 2‐point step size gradient method for CBCT reconstructions and show its clinical feasibility. Methods: The Barzilai‐Borwein (BB) 2‐point step size gradient method is getting recent attentions for accelerating Total Variation (TV) based CBCT reconstructions. In order to become truly viable for clinical applications, however, the iterative framework needs to ensure guaranteed convergence by carefully defining the cost function and the reconstruction algorithm. We propose a novel approach that combines an unconstrained BB (UBB) method and the gradient projection (GP) method enforcing non‐negativity constraints. This way, the proposed GP‐UBB algorithm inherits both the fast converging property of the UBB and the robust convergence property of GP. We applied this algorithm to both Shepp‐Logan numerical phantom and a clinically‐treated head‐and‐neck patient acquired from the TrueBeam system (Varian Medical Systems, Palo Alto, CA). Furthermore, we accelerated the reconstruction by implementing the algorithm on NVIDIA GTX 295 GPU card. Results: We first compared GPUBB with a recently proposed BB‐ based CBCT reconstruction method available in the literature and the well‐ known ASD‐POCS algorithm using Shepp‐Logan numerical phantom with 40 projections. As the iterations progress, GPUBB is found to converge much faster than the other two algorithms. Therefore, GPUBB commands superior image quality with less number of iterations. We then applied the algorithm to a clinically‐treated head‐and‐neck patient. It was observed that, compared with the FDK algorithm with 364 projections, our GPUBB algorithm produces a visually equivalent quality CBCT image with only 120 projections, further supporting its practical value for realizing low‐dose iterative CBCT reconstructions. Conclusions: By developing a novel, fast converging 2‐step size gradient method for a CBCT reconstruction problem, we enhanced the clinical applicability of the compressive sensing based iterative reconstruction by guaranteeing convergence (i.e., consistent reconstructions) and accelerating the reconstruction speed (i.e., less number of iterations).