This paper presents a demosaicking method based on high-order interpolation with parameters. Demosaicking is an essential process in capturing color images through a single sensor-array. Thus, a lot of methods including the Hamilton-Adams(HA) method has been studied in this literature. However, the image quality depends on various factors such as contrast and correlation in color space; existing algorithms depend on test images in use. Consequently, a new test image set was suggested to develop demosaicking algorithms properly. According to previous studies, the HA method shows high performances with the new test data set. In this paper, we improve the HA method using high-order interpolation with parameters. Also, we provide an analysis and formulations for the proposed method. To evaluate our method, we compare our method with the existing methods both objectively and subjectively. The experimental results indicate that the proposed method is superior to the existing methods.