<p>Accelerated proximal gradient methods have become a useful tool in large-scale convex optimization, especially for variational regularization with non-smooth priors. Prevailing convergence analysis considers that users can perform the proximal and the gradient steps exactly. Still, in some practical applications, these steps often need to be computed inexactly, which may slow down convergence or even lead to divergence. Researchers have developed theoretical frameworks for convergence under the inexactness of computations to handle this issue. For example, Bello-Cruz et al. [On FISTA with a relative error rule, Comput. Optim. Appl. 84(2):295–318, 2023] developed a relative error rule to be used with inexact FISTA (Fast Iterative Soft-Thresholding Algorithm). Their technique works whenever suitable stepsizes are known. In the present paper, we study the convergence of inexact FISTA with line search. We develop an adaptive line search without demanding any additional effort as compared with non-adaptive line search approaches. The computational performance is illustrated for an important category of problems with simulated tomographic data. Both theoretical results and numerical experiments indicate that the proposed method is effective for variational regularization in inverse problems.</p>