Human activity recognition (HAR) techniques are playing a significant role in monitoring the daily activities of human life such as elderly care, investigation activities, healthcare, sports, and smart homes. Smartphones incorporated with varieties of motion sensors like accelerometers and gyroscopes are widely used inertial sensors that can identify different physical conditions of human. In recent research, many works have been done regarding human activity recognition. Sensor data of smartphone produces high dimensional feature vectors for identifying human activities. However, all the vectors are not contributing equally for identification process. Including all feature vectors create a phenomenon known as 'curse of dimensionality'. This research has proposed a hybrid method feature selection process, which includes a filter and wrapper method. The process uses a sequential floating forward search (SFFS) to extract desired features for better activity recognition. Features are then fed to a multiclass support vector machine (SVM) to create nonlinear classifiers by adopting the kernel trick for training and testing purpose. We validated our model with a benchmark dataset. Our proposed system works efficiently with limited hardware resource and provides satisfactory activity identification.