This paper proposes an intelligent image interpolation method based on Cubic Hermite procedure for improving digital images. Image interpolation has been used to create high-resolution effects in digitized image data, providing sharpness in high frequency image data and smoothness in low frequency image data. Most interpolation techniques proposed in the past are centered on determining pixel values using the relationship between neighboring points. As one of the more prevalent interpolation techniques, Cubic Hermite procedure attains the interpolation with a 3rd order polynomial fit using derivatives of points and adaptive smoothness parameters. Cubic Hermite features many forms of a curved shape, which effectively reduce the problems inherent in interpolations. This paper focuses on a method that intelligently determines the derivatives and adaptive smoothness parameters to effectively contain the interpolation error, achieving significantly improved images. Derivatives are determined by taking a weighted sum of the neighboring points whose weighting function decreases as the intensity difference of neighboring points increases. Smoothness parameter is obtained by training an exemplar image to fit into the Cubic Hermite function such that the interpolation error is minimized at each interpolating point. The simulations indicate that the proposed method achieves improved image results over that of conventional methods in terms of error and image quality performance.