Abstract: The existing method of boundaries continuity preserving loses the data compression property due to inserting all deleted knots.In this paper,two methods to preserve the curve boundary continuity during wavelet transform are presented.One is inserting knots related with C^r continuity and then adjusting the corresponding control points to be consistent with high resolution curve;the other is directly adjusting the control points related with C^r continuity.In terms of surface,the surface splitting method and the T surface method are presented: the surface is divided into the parts of boundary and center,inserting knots in the part of boundary and then adjusting the corresponding control points to be consistent with high resolution surface;T-mesh is constructed,which part of boundary and center is consistent with high resolution and low resolution surface respectively.The T-surface boundary preserving method is extended to the closed B-spline surface wavelet transform.The experimental results demonstrate that the methods in this paper are not only preserving the boundaries continuity in the wavelet transform,but also retaining the data compression property.