Advances in the medical applications of brain-computer interface, like the motor imagery systems, are highly contributed to making the disabled live better. One of the challenges with such systems is to achieve high classification accuracy. A highly accurate classification algorithm with low computational complexity is proposed here to classify different motor imageries and execution tasks. An experimental study is performed on two electroencephalography datasets (Iranian Brain-Computer Interface competition [iBCIC] dataset and the world BCI Competition IV dataset 2a) to validate the effectiveness of the proposed method. For lower complexity, the common spatial pattern is applied to decrease the 64 channel signal to four components, in addition to increase the class separability. From these components, first, some features are extracted in the time and time-frequency domains, and next, the best linear combination of these is selected by adopting the stepwise linear discriminant analysis (LDA) method, which are then applied in training and testing the classifiers including LDA, random forest, support vector machine, and K nearest neighbors. The classification strategy is of majority voting among the results of the binary classifiers. The experimental results indicate that the proposed algorithm accuracy is much higher than that of the winner of the first iBCIC. As to dataset 2a of the world BCI competition IV, the obtained results for subjects 6 and 9 outperform their counterparts. Moreover, this algorithm yields a mean kappa value of 0.53, which is higher than that of the second winner of the competition. The results indicate that this method is able to classify motor imagery and execution tasks in both effective and automatic manners.