Restricted Boltzmann Machine (RBM) has been applied to a wide variety of tasks due to its advantage in feature extraction. Implementing sparsity constraint in the activated hidden units of RBM is an important improvement on RBM. The sparsity constraints in the existing methods are usually specified by users and are independent of the input data. However, the input data could be heterogeneous in content and thus naturally demand elastic and adaptive settings of the sparsity constraints. To solve this problem, we proposed a generalized model with adaptive sparsity constraint, named Gaussian Cardinality Restricted Boltzmann Machines (GC-RBM). In this model, the thresholds of hidden unit activations are decided by the input data and a given Gaussian distribution on the pre-training phase. We provide a principled method to train the GC-RBM with Gaussian prior. Experimental results on two real world data sets justify the effectiveness of the proposed method and its superiority over CaRBM in terms of classification accuracy.