For the problem of finding the shortest paths from a prescribed vertex to the other vertices in a given network with nonnegative arc lengths, we investigate practical efficiencies of typical existing algorithms, i.e., the label-correcting method with a FIFO and that of a two-way sequence, and the label-setting method with a heap and that with a 1- or 2-level bucket system. We propose also a new method with a variable bucket system and compare it with those existing methods. Among the existing methods, the label-correcting method of a two-way sequence and the label-setting method with a I-level bucket system have been found efficient in most cases. The new proposed method is not only as efficient as those but it is also robust for a large variety of networks, so that it may be recommended for practical use.