In this paper, we have formulated a Laplacian Least Squares Twin Support Vector Machine called Lap-LST-KSVC for semi-supervised multi-category k-class classification problem. Similar to Least Squares Twin Support Vector Machine for multi-classification(LST-KSVC), Lap-LST-KSVC, evaluates all the training samples into “1-versus-1-versus-rest” classification paradigm, so as to generate ternary output {−1, 0, +1}. Experimental results prove the efficacy of the proposed method over other inline Laplacian Twin Support Vector Machine(Lap-TWSVM) in terms of classification accuracy and computational time.