Predicting remaining useful life (RUL) of machinery is of vital importance to prognostics and health management. Reliable and accurate RUL prediction not only can reduce maintenance costs and increase machine availability but also even prevent catastrophic consequences. In reality, RUL predictions usually require numerous certain kinds of machine degradation data. However, complex operating conditions and safety issues may often result in fragmented data records generated, with very few complete samples being usable. To overcome the challenge of RUL prediction with limited data, this paper proposes a novel MetaDESK model that is based on meta-learning with deep sparse kernel network. The general idea is to train a sparse kernel with a variational posterior in a data-driven fashion, and then transfer it to a new few-shot RUL task via meta-knowledge. Specifically, we first incorporate a Gaussian Process into the model-agnostic meta-learning (MAML) framework and use variational inference to estimate latent variables as kernel features, which allows us to sample from a non-Gaussian distribution of the posterior. Then, the KL-divergence of sparse approximation is added to the kernel features as a regularization term through inference to reduce the overfitting problem. Also, to exploit the dependencies of the tasks we integrate both their shared knowledge and task-specific information into a contextual reasoning process, which is implemented by a bidirectional long short-term memory network. To evaluate our proposed model, we conduct extensive experiments using publicly available degradation data, and the results verify the model's effectiveness.