Propositional satisfiability (SAT) is an NP-complete problem that impacts manyresearch fields, such as planning, verification, and security. Mainstream modernSAT solvers are based on the Conflict-Driven Clause Learning (CDCL) algorithm.Recent work aimed to enhance CDCL SAT solvers using Graph Neural Networks(GNNs). However, so far this approach either has not made solving more effective,or required substantial GPU resources for frequent online model inferences. Aimingto make GNN improvements practical, this paper proposes an approach calledNeuroBack, which builds on two insights: (1) predicting phases (i.e., values) ofvariables appearing in the majority (or even all) of the satisfying assignments areessential for CDCL SAT solving, and (2) it is sufficient to query the neural modelonly once for the predictions before the SAT solving starts. Once trained, theoffline model inference allows NeuroBack to execute exclusively on the CPU,removing its reliance on GPU resources. To train NeuroBack, a new dataset calledDataBack containing 120,286 data samples is created. Finally, NeuroBack is implementedas an enhancement to a state-of-the-art SAT solver called Kissat. As a result,it allowed Kissat to solve 5.2% more problems on the recent SAT competitionproblem set, SATCOMP-2022. NeuroBack therefore shows how machine learningcan be harnessed to improve SAT solving in an effective and practical manner.