The original guided image filter algorithm performs not robust enough because it occupies the same local linear model among all the local patches while ignoring the texture difference. Based on the absolute magnitude of LoG (Laplacian-of-Gaussian) strength, a locally adaptive weighting parameter was used to penalize the fixed regularization parameter to produce a more robust method, aiming to amplify the grey scale difference between flat patch and edge patch, meanwhile avoid degraded denoising performance of original method. The open medical database BrainWeb including 6 T1, 6 T2 and 6 PD weighted pictures added with 9% magnitude of Racian noise were used as the testing database. Structural Similarity Index Measurement (SSIM) and Cumulative Probability of Blur Detection (CPBD) were used as quantity value indexes. According to the best experiment results, the proposed method respectively gets 5% and 6% advancement for SSIM and CPBD, compared to original guided image filter algorithm. Furthermore, the proposed method performs better than both the original guided image filter and another improved guided image filter under each regularization parameter of guided image filter, and the original O( N) time complexity is not affected. Compared to state-of-the-art methods, the proposed method obtains best performance compromising SSIM and CPBD, and it has lowest time complexity, while providing a fast and robust denoising method for medical images and color images.