This paper deals with the classification of grassland management practices 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 scale by modeling its pixels distributions by a Gaussian distribution. To measure the similarity between two grasslands, a Gaussian mean map kernel is proposed as a second contribution: the α-Gaussian mean kernel. It allows to weight the influence of the covariance matrix when comparing two grasslands. This kernel is used in Support Vector Machine for the supervised classification of three management practice types in 52 grasslands from southwest France, using an intra-annual multispectral time series of Formosat-2 satellite. Results in terms of classification accuracy and processing time are compared to other pixel-and object-based approaches. The proposed modeling showed to be the best compromise between processing speed and classification accuracy. It can adapt to the classification constraints and it encompasses several similarity measures known in the literature.