A multitargeted therapeutic approach with hybrid drugs is a promising strategy to enhance anticancer efficiency and overcome drug resistance in nonsmall cell lung cancer (NSCLC) treatment. Estimating affinities of small molecules against targets of interest typically proceeds as a preliminary action for recent drug discovery in the pharmaceutical industry. In this investigation, we employed machine learning models to provide a computationally affordable means for computer-aided screening to accelerate the discovery of potential drug compounds. In particular, we introduced a quantitative structure–activity-relationship (QSAR)-based multitask learning model to facilitate an in silico screening system of multitargeted drug development. Our method combines a recently developed graph-based neural network architecture, principal neighborhood aggregation (PNA), with a descriptor-based deep neural network supporting synergistic utilization of molecular graph and fingerprint features. The model was generated by more than ten-thousands affinity-reported ligands of seven crucial receptor tyrosine kinases in NSCLC from two public data sources. As a result, our multitask model demonstrated better performance than all other benchmark models, as well as achieving satisfying predictive ability regarding applicable QSAR criteria for most tasks within the model’s applicability. Since our model could potentially be a screening tool for practical use, we have provided a model implementation platform with a tutorial that is freely accessible hence, advising the first move in a long journey of cancer drug development.