Curve extension is a useful tool in the computer‐aided design (CAD) community. A given B‐spline curve usually needs to be extended by another curve to reach one or more target points. In this work, we aim to enlarge the representation domain of the extending part to achieve the optimal extending result in the global solution space. Inspired by this, we have made three contributions. First, we use piecewise polynomial, that is, a nonuniform B‐spline, instead of one polynomial segment to extend the original curve. Compared to one polynomial segment, curves consisting of piecewise polynomial have stronger modeling ability and therefore expand the solution space of the problem. For extension to multiple target points, we are the first to directly give extension results based on all target points rather than extending to every target step by step. Third, we exploit the matrix representation of B‐splines to obtain an explicit solution for this extension problem. The detailed formula derivations and experimental results are provided to show the validity and effectiveness of our method.