This article presents the development of machine-learning-enabled data-driven models for effective capacity predictions for lithium-ion (Li-ion) batteries under different cyclic conditions. To achieve this, a model structure is first proposed with the considerations of battery aging tendency and the corresponding operational temperature and depth-of-discharge. Then based on a systematic understanding of the covariance functions within the Gaussian process regression (GPR), two related data-driven models are developed. Specifically, by modifying the isotropic squared exponential kernel with an automatic relevance determination structure, "Model A" could extract the highly relevant input features for capacity predictions. Through coupling the Arrhenius law and a polynomial equation into a compositional kernel, "Model B" is capable of considering the electrochemical and empirical knowledge of battery degradation. The developed models are validated and compared on the nickel-manganese-cobalt (NMC) oxide Li-ion batteries with various cycling patterns. The experimental results demonstrate that the modified GPR model considering the battery electrochemical and empirical aging signature outperforms other counterparts and is able to achieve satisfactory results for both one-step and multistep predictions. The proposed technique is promising for battery capacity predictions under various cycling cases.