We study the dynamic version of the distributed all-pairs shortest paths problem. Most of the solutions given in the literature for this problem, either (i) work under the assumption that before dealing with an edge operation, the algorithm for the previous operation has to be terminated, that is, they are not able to update shortest paths concurrently, or (ii) concurrently update shortest paths, but their convergence can be very slow (possibly infinite). In this paper we propose a partially dynamic algorithm that overcomes these limitations. In particular, it is able to concurrently update shortest paths and its convergence is quite fast