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Conditional text generation is supposed to generate a fluent and coherent target text that is faithful to the source text. Although pre-trained models have achieved promising results, they still suffer from the crucial factuality problem. To deal with this issue, we propose a factuality-aware pretraining-finetuning framework named FactGen, which fully considers factuality during two training stages. Specifically, at the pre-training stage, we utilize a natural language inference model to construct target texts that are entailed by the source texts, resulting in a more factually consistent pre-training objective. Then, during the fine-tuning stage, we further introduce a contrastive ranking loss to encourage the model to generate factually consistent text with higher probability. Extensive experiments on three conditional text generation tasks demonstrate the effectiveness and generality of our training framework.