Phillips q-Bézier curves are a class of generalized Bézier curves containing q-integers. The research was conducted on the curvature monotonicity condition of quadratic Phillips q-Bézier curve from two aspects of algebra and geometry. Based on this, the following two curves were constructed: a quadratic Phillips q-Bézier curve with monotonous curvature and a combined quadratic Phillips q-Bézier curve with decreasing curvature. Firstly, through the coordinate representation of curve curvature, this paper explored the condition of monotonic curvature in algebraic form. By defining the curvature decreasing (or increasing) bounding circle, the geometric sufficient and necessary conditions were given to enable decreasing (or increasing) curvature for quadratic Phillips q-Bézier curves. In the case of the shape parameter q=1, Phillips q-Bézier curves would degenerate into classical Bézier curves. Thus, the curvature monotonicity conditions of quadratic Phillips q-Bézier curves include the results of classical quadratic Bézier curves. Secondly, the paper examined the G 2 smooth condition of quadratic Phillips q-Bézier curves and the influence of parameters on the stitching curve. Thirdly, for the quadratic Phillips q-Bézier curve with given initial and final control vertices, the appropriate intermediate control vertex was selected, the range of shape parameters was obtained in the case of decreasing (or increasing) curvature, and a quadratic Phillips q-Bézier curve with decreasing (or increasing) curvature was constructed. Furthermore, a combined quadratic Phillips q-Bézier curve was constructed, which could satisfy both G 2 smooth condition and decreasing curvature. Finally, using the combined quadratic Phillips q-Bézier curve with decreasing curvature, the transition curve between two circles with inclusion relationship was constructed. The numerical examples highlight the advantages and flexibility of the combinatorial quadratic Phillips q-Bézier curve in modeling.