Life prediction of lithium-ion batteries is vital for battery system utilization and maintenance. Especially, the accurate life prediction in early cycles can accelerate the battery design, production, and optimization. However, diverse aging mechanisms, various cycle profiles, and negligible capacity degradation in the early cycling stages pose significant challenges. This paper proposes a novel deep learning-based life prediction method for lithium-ion batteries with strong generalization capability under multiple cycle profiles, where the battery lifetime model is formulated by a two-dimensional and one-dimensional parallel hybrid neural network. Firstly, the input data is constructed by a five-step streamlined preprocessing approach. Secondly, two-dimensional and one-dimensional convolutional neural networks are respectively used to extract the underlying associations between the data. Then, the long short-term memory network is employed to learn the time-sequential relationships among the extracted features. Ultimately, the diagnosis for the current cycle life and the prognostic on the remaining useful life of the battery are performed. A well-known dataset is utilized to validate the accuracy and generalization performance of the proposed method. Comparison results with other methods show that the proposed model has strong generalization capability. For the test set composed of data from 31 cells under 25 different cycle profiles, its mean absolute percentage error in early lifetime prediction and remaining useful life prediction is merely 1.47% and 2.85%.