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With the aim to tackle the problem that the engineering complex curves can not be constructed by using a single curve, the continuity condition of the λ-Bézier curves of degree n with shape control parameters were investigated. The λ-Bézier curves of degree n not only inherit the outstanding properties of the corresponding classical Bézier curve of degree n, but also have a good performance on adjusting their shapes by changing shape control parameters. In the particular case where the shape control parameter equals to zero, the λ-Bézier curves degenerate to the classical Bézier curve. Firstly, the Bernstein-like basis functions of arbitrary order n were constructed by using a recursive formula from the initial basis functions, and the geometric property at the endpoints of the λ-Bézier curves were obtained, such as interpolation at the corners, the derivative at end-points and the second derivative at end-points. Secondly, based on the analysis of basis functions and terminal properties, the necessary and sufficient conditions of G1, G2 continuity and C1,C2 continuity between two adjacent λ-Bézier curves were proposed. Finally, some properties of the continuity condition for the λ-Bézier curves and applications in λ-Bézier curves design were discussed. In addition, the influence rules of the shape parameters on the complex λ-Bézier curves shape were studied.The modeling examples showed that the proposed method was effective and easy to implement, which greatly enhanced the ability to construct complex curves by using λ-Bézier curves.