Based on an efficient generic position checking method and on a method to solve bivariate polynomial systems,we present a new and efficient algorithm to compute the topology of an algebraic space curve.In the new algorithm,the topology computation of an algebraic space curve is transformed into the topology computation of two algebraic plane curves.We also give an ε-meshing of the space curve after we obtain its topology.Many nontrivial experiments show the efficiency of the algorithm.It is a joint work with Kai Jin.