This paper concerns robust and reliable speaker model training for text-independent speaker verification. The baseline speaker modeling approach is the Gaussian mixture model (GMM). In text-independent speaker verification, the amount of speech data may be different for speakers. However, we still wish the modeling approach to perform equally well for all speakers. Besides, the modeling technique must be least vulnerable against unseen data. A traditional approach for GMM training is expectation maximization (EM) method, which is known for its overfitting problem and its weakness in handling insufficient training data. To tackle these problems, variational approximation is proposed. Variational approaches are known to be robust against overtraining and data insufficiency. We evaluated the proposed approach on two different databases, namely KING and TFarsdat. The experiments show that the proposed approach improves the performance on TFarsdat and KING databases by 0.56% and 4.81%, respectively. Also, the experiments show that the variationally optimized GMM is more robust against noise and the verification error rate in noisy environments for TFarsdat dataset decreases by 1.52%.