This paper is concerned with an initial-boundary problem of nonconvex scalar conservation laws with two pieces of constant initial data and constant boundary data. Under the condition that the flux function has one inflection point, by the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method for the global weak entropy solution of the initial-boundary value problem and clarify the solution structure nearby the boundary. In contrast to the initial-boundary value problem for strictly convex scalar conservation laws, the weak entropy solution of the initial-boundary value problem for nonconvex scalar conservation laws includes the following new interaction type: a contact or non-contact shock collides with the boundary and a new non-contact shock wave rebounds from the boundary.