Typically, voice conversion is regarded as an engineering problem with limited training data. The reliance on massive amounts of data hinders the practical applicability of deep learning approaches, which have been extensively researched in recent years. On the other hand, statistical methods are effective with limited data but have difficulties in modelling complex mapping functions. This paper proposes a voice conversion method that works with limited data and is based on stochastic variational deep kernel learning (SVDKL). At the same time, SVDKL enables the use of deep neural networks' expressive capability as well as the high flexibility of the Gaussian process as a Bayesian and non-parametric method. When the conventional kernel is combined with the deep neural network, it is possible to estimate non-smooth and more complex functions. Furthermore, the model's sparse variational Gaussian process solves the scalability problem and, unlike the exact Gaussian process, allows for the learning of a global mapping function for the entire acoustic space. One of the most important aspects of the proposed scheme is that the model parameters are trained using marginal likelihood optimization, which considers both data fitting and model complexity. Considering the complexity of the model reduces the amount of training data by increasing the resistance to overfitting. To evaluate the proposed scheme, we examined the model's performance with approximately 80 seconds of training data. The results indicated that our method obtained a higher mean opinion score, smaller spectral distortion, and better preference tests than the compared methods.