In image processing, it is often desirable to remove the noise and preserve image features. Due to the strong edge preserving ability, the total variation (TV) based regularization has been widely studied. However, it produces undesirable staircase effect. To alleviate the staircase effect, the LOT model proposed by Lysaker et al. (IEEE Trans Image Process 13(10): 1345-1357, 2004) has been studied, which is called the two-step method. After that, this method has started to appear as one of the more effective methods for image denoising, which includes two energy functions: one is about the normal field, the other is about the reconstruction image using the normal field obtained in the first step. However, the smoothed normal field is only related to the original noisy image in the first step, which is not enough. In this paper, we proposed a modified LOT model for image denoising, which lets the reconstruction vector field be related to the restored image. In addition, to compute the new model, we design a relaxed alternative direction method. The numerical experiments show that the new model can obtain the better results compared with some state-of-the art methods.