We construct an Abel-Jacobi type map on the homologically trivial part of Lawson homology groups. It generalizes the Abel-Jacobi map constructed by Griffiths. By using a result of H. Clemens, we answer affirmatively the question whether there exists a smooth projective complex variety with infinitely generated Lawson homology groups LpH2p+k(X,Q) when k>0. As a corollary, we find, for any nonnegative integer j, a smooth complex projective variety X carrying infinitely generated semi-topological K-groups Ksstj(X)Q.