Lithium-ion batteries have been widely used in electric vehicles, smart grids and many other applications as energy storage devices, for which the aging assessment is crucial to guarantee their safe and reliable operation. The battery capacity is a popular indicator for assessing the battery aging, however, its accurate estimation is challenging due to a range of time-varying situation-dependent internal and external factors. Traditional simplified models and machine learning tools are difficult to capture these characteristics. As a class of deep neural networks, the convolutional neural network (CNN) is powerful to capture hidden information from a huge amount of input data, making it an ideal tool for battery capacity estimation. This paper proposes a CNN-based battery capacity estimation method, which can accurately estimate the battery capacity using limited available measurements, without resorting to other offline information. Further, the proposed method only requires partial charging segment of voltage, current and temperature curves, making it possible to achieve fast online health monitoring. The partial charging curves have a fixed length of 225 consecutive points and a flexible starting point, thereby short-term charging data of the battery charged from any initial state-of-charge can be used to produce accurate capacity estimation. To employ CNN for capacity estimation using partial charging curves is however not trivial, this paper presents a comprehensive approach covering time series-to-image transformation, data segmentation, and CNN configuration. The CNN-based method is applied to two battery degradation datasets and achieves root mean square errors (RMSEs) of less than 0.0279 Ah (2.54%) and 0.0217 Ah (2.93% ), respectively, outperforming existing machine learning methods.