Head motion may unexpectedly occur during a CT scan. It thereby results in motion artifacts in a reconstructed image and may lead to a false diagnosis or a failure of diagnosis. To alleviate this motion problem, as a hardware approach, increasing the gantry rotation speed or using an immobilization device is usually considered. These approaches, however, cannot completely resolve the motion problem. Hence, motion estimation (ME) and compensation for it have been explored as a software approach instead. In this paper, adopting the latter approach, we propose a head motion correction algorithm in helical CT scanning, based on filtered backprojection (FBP). For the motion correction, we first introduce a new motion-compensated (MC) reconstruction scheme based on FBP, which is applicable to helical scanning. We then estimate the head motion parameters by using an iterative nonlinear optimization algorithm, or the L-BFGS. Note here that an objective function for the optimization is defined on reconstructed images in each iteration, which are obtained by using the proposed MC reconstruction scheme. Using the estimated motion parameters, we then obtain the final MC reconstructed image. Using numerical and physical phantom datasets along with simulated head motions, we demonstrate that the proposed algorithm can provide significantly improved quality to MC reconstructed images by alleviating motion artifacts.