Gesture-based interaction, as a natural way for human-computer interaction, has a wide range of applications in ubiquitous computing environment. This paper presents an acceleration-based gesture recognition approach, called FDSVM (Frame-based Descriptor and multi-class SVM), which needs only a wearable 3-dimensional accelerometer. With FDSVM, firstly, the acceleration data of a gesture is collected and represented by a frame-based descriptor, to extract the discriminative information. Then a SVM-based multi-class gesture classifier is built for recognition in the nonlinear gesture feature space. Extensive experimental results on a data set with 3360 gesture samples of 12 gestures over weeks demonstrate that the proposed FDSVM approach significantly outperforms other four methods: DTW, Naïve Bayes, C4.5 and HMM. In the user-dependent case, FDSVM achieves the recognition rate of 99.38% for the 4 direction gestures and 95.21% for all the 12 gestures. In the user-independent case, it obtains the recognition rate of 98.93% for 4 gestures and 89.29% for 12 gestures. Compared to other accelerometer-based gesture recognition approaches reported in literature FDSVM gives the best resulrs for both user-dependent and user-independent cases.