Presence of hair in psoriasis skin images may adversely affect the extraction of the features required for computer aided analysis, thus compromise the detection and diagnostic results. Therefore, for the diagnosis of psoriasis to be accurate, it is vitally important to remove hair, if it exists, from images in the preprocessing stage. This paper presents, for the first time, a hair detection and removal algorithm for 2D psoriasis images. The hair removal process starts with a markers removal algorithm, where the shape features are extracted from the binary input image. The outcome of this step is removal of all objects that obscure the image lesions such that the output image contains psoriasis lesions and normal skin only. Next, the dark hair in the skin is identified using contrast enhancement method and morphological operations. Finally, image interpolation is performed to replace the hair pixels with hair free neighbouring pixels values through image inpainting. The proposed algorithm is tested on 64 psoriasis images acquired from the Royal Melbourne Hospital, Victoria, Australia. Experimental results demonstrate that the algorithm is highly accurate and effective. In addition, the widely used hair removal software DullRazor® is used on the same 64 images for comparison. The results show that our proposed algorithm performs quite well and is more adapt to psoriasis images. The method is more effective because it overcomes the problem of removing skin hair without affecting the intensity or texture features of the lesions.