Many recent applications of computer graphics and human computer interaction have adopted both colour cameras and depth cameras as input devices. Therefore, an effective calibration of both types of hardware taking different colour and depth inputs is required. Our approach removes the numerical difficulties of using non-linear optimization in previous methods which explicitly resolve camera intrinsics as well as the transformation between depth and colour cameras. A matrix of hybrid parameters is introduced to linearize our optimization. The hybrid parameters offer a transformation from a depth parametric space (depth camera image) to a colour parametric space (colour camera image) by combining the intrinsic parameters of depth camera and a rotation transformation from depth camera to colour camera. Both the rotation transformation and intrinsic parameters can be explicitly calculated from our hybrid parameters with the help of a standard QR factorisation. We test our algorithm with both synthesized data and real-world data where ground-truth depth information is captured by Microsoft Kinect. The experiments show that our approach can provide comparable accuracy of calibration with the state-of-the-art algorithms while taking much less computation time (1/50 of Herrera's method and 1/10 of Raposo's method) due to the advantage of using hybrid parameters.