Pipe Link, which is a pencil-and-paper puzzle introduced by Japanese puzzle publisher Nikoli, is played on a rectangular grid of squares. We studied the computational complexity of Pipe Link, and this paper shows that the problem to decide if a given instance of Pipe Link has a solution is NP-complete by a reduction from the Hamiltonian circuit problem for a given planar graph with a degree of at most 3. Our reduction is carefully designed so that we can also prove ASP-completeness of the another-solution-problem.