This paper deals with the classification of grasslands using high resolution satellite image time series. Grasslands considered in this work are semi-natural elements in fragmented landscapes, i.e., they are heterogeneous and small elements. The first contribution of this study is to account for grassland heterogeneity while working at the object level by modeling its pixels distributions by a Gaussian distribution. To measure the similarity between two grasslands, a new kernel is proposed as a second contribution: the α -Gaussian mean kernel. It allows one to weight the influence of the covariance matrix when comparing two Gaussian distributions. This kernel is introduced in support vector machines for the supervised classification of grasslands from southwest France. A dense intra-annual multispectral time series of the Formosat-2 satellite is used for the classification of grasslands’ management practices, while an inter-annual NDVI time series of Formosat-2 is used for old and young grasslands’ discrimination. Results are compared to other existing pixel- and object-based approaches in terms of classification accuracy and processing time. The proposed method is shown to be a good compromise between processing speed and classification accuracy. It can adapt to the classification constraints, and it encompasses several similarity measures known in the literature. It is appropriate for the classification of small and heterogeneous objects such as grasslands.