Smooth twin support vector machines (STWSVM) uses Sigmoid function to transform the unsmooth twin support vector machines (TWSVM) into smooth ones. However, because of the low approximation ability of Sigmoid function, the classification accuracy of STWSVM is unsatisfactory. Furthermore, similar to TWSVM, STWSVM is sensitive to the abnormal samples. In order to address the above problems, this paper introduces CHKS function, and proposes a smooth twin support vector machines, smooth CHKS twin support vector machines (SCTWSVM). In order to reduce the influence of abnormal samples on SCTWSVM, different importance are given for each training sample according to the sample point positions for SCTWSVM, resulting in weighted smooth CHKS twin support vector machines (WSCTWSVM). The study proves that SCTWSVM is not only strictly convex, but also can meet the arbitrary order smooth performance. Meanwhile, the experimental results show that SCTWSVM has better performance than STWSVM. Furthermore, the experimental results also show that WSCTWSVM is effective and feasible relative to SCTWSVM.