  We present a deterministic distributed algorithm to compute all-pairs
shortest paths(APSP) in an edge-weighted directed or undirected graph. Our
algorithm runs in $\tilde{O}(n^{3/2})$ rounds in the Congest model, where $n$
is the number of nodes in the graph. This is the first $o(n^2)$ rounds
deterministic distributed algorithm for the weighted APSP problem. Our
algorithm is fairly simple and incorporates a deterministic distributed
algorithm we develop for computing a `blocker set' \cite{King99}, which has
been used earlier in sequential dynamic computation of APSP.
