In this paper we present a novel approach to construct B-spline wavelets under constraints, taking advantage of the lifting scheme. Constrained B-spline wavelets allowmultiresolution analysis of B-splines which fixes positions, tangents and/or high order derivatives at some user specified parameter values, thus extend the ability of B-spline wavelets: smoothing a curve while preserving user specified "feature points"; representing several segments of a single curve at different resolution levels, leaving no awkward "gaps"; multiresolution editing of B-spline curves under constraints. For a given B-spline order and the number of constraints, both the time and storage complexities of our algorithm are linear in the number of control points. This feature makes our algorithm extremely suitable for large scale datasets.