For the problem of imbalanced data classification which was not discussed in the standard Extreme Support Vector Machines (ESVM), an imbalanced extreme support vector machines (IESVM) was proposed. Firstly, a preliminary normal vector of separating hyperplane is obtained directly by geometric analysis. Secondly, penalty factors are obtained which are based on the information provided by data sets projecting onto the preliminary normal vector. Finally, the final separation hyperplane is got through the improved ESVM training. IESVM can overcome disadvantages of traditional designing methods which only consider the imbalance of samples size and can improve the generalization ability of ESVM. Experimental results show that the method can effectively enhance the classification performance on imbalanced data sets.