Approximate Bayesian computing (ABC) is a likelihood-free method that has grown increasingly popular since early applications in population genetics. However, the theoretical justification for inference based on this method has yet to be fully developed especially pertaining to the use of non-sufficient summary statistics. We introduce a more general computational technique, approximate confidence distribution computing (ACC) to overcome a few issues associated with the ABC method, for instance, the lack of theory supporting the use of non-sufficient summary statistics, the lack of guardian for the selection of prior, and the long computing time. Specifically, we establish frequentist coverage properties for the outcome of the ACC method by using the theory of confidence distributions, and thus inference based on ACC is justified, even if reliant upon a non-sufficient summary statistic. We supplement the theory with simulation studies and an epidemiological application and demonstrate that a well-tended ACC algorithm can be more computationally efficient than a typical ABC algorithm.