Lung cancer is the leading cause of cancer deaths. Low-dose computed tomography (CT) screening has been shown to significantly reduce lung cancer mortality but suffers from a high false positive rate that leads to unnecessary diagnostic procedures. The development of deep learning techniques has the potential to help improve lung cancer screening technology. Here we present the algorithm, DeepScreener, which can predict a patient's cancer status from a volumetric lung CT scan. DeepScreener is based on our model of Spatial Pyramid Pooling, which ranked 16th of 1972 teams (top 1%) in the Data Science Bowl 2017 (DSB2017) competition, evaluated with the challenge datasets. Here we test the algorithm with an independent set of 1449 low-dose CT scans of the National Lung Screening Trial (NLST) cohort, and we find that DeepScreener has consistent performance of high accuracy. Furthermore, by combining Spatial Pyramid Pooling and 3D Convolution, it achieves an AUC of 0.892, surpassing the previous state-of-the-art algorithms using only 3D convolution. The advancement of deep learning algorithms can potentially help improve lung cancer detection with low-dose CT scans.