Accurate reconstruction of computed tomography (CT) images is crucial in medical imaging field. However, there are unavoidable interpolation errors in the backprojection step of the conventional reconstruction methods, i.e., filtered-back-projection based methods, which are detrimental to the accurate reconstruction. In this study, to address this issue, we propose a novel deep learning model, named Leanable-Interpolation-based FBP or LInFBP shortly, to enhance the reconstructed CT image quality, which achieves learnable interpolation in the backprojection step of filtered backprojection (FBP) and alleviates the interpolation errors. Specifically, in the proposed LInFBP, we formulate every local piece of the latent continuous function of discrete sinogram data as a linear combination of selected basis functions, and learn this continuous function by exploiting a deep network to predict the linear combination coefficients. Then, the learned latent continuous function is exploited for interpolation in backprojection step, which first time takes the advantage of deep learning for the interpolation in FBP. Extensive experiments, which encompass diverse CT scenarios, demonstrate the effectiveness of the proposed LInFBP in terms of enhanced reconstructed image quality, plug-and-play ability and generalization capability.