We propose SP-NLG: A semantic-parsing-guided natural language generation framework for logical content generation with high fidelity. Prior studies adopt large pretrained language models and coarse-to-fine decoding techniques to generate text with logic; while achieving considerable results on automatic evaluation metrics, they still face challenges in terms of logical fidelity based on human evaluation. Inspired by semantic parsing, which translates natural language utterances into executable logical forms, we propose to guide the generation process with a semantic parser. Different from semantic parsing and QA tasks, of which the logical correctness can be evaluated based on the execution result, the logic information of the generated content is implicit. To leverage a semantic parser for generation, we propose a slot-tied back-search algorithm. We follow the coarse-to-fine generation scheme, but instead of filling the slots with model predictions, which is less uncontrolled, the slot values are offline searched by the algorithm. The slot-tied back-search algorithm ties the parameters of a logic form with the slots of a template in one-to-one correspondence. We back-search the arguments that correctly execute the logic form and fill the arguments (as slot values) into the textual template to generate the final target, which ensures the logical correctness. Experiment results of a model built on SP-NLG demonstrates that our framework achieves high fidelity on logical text generation.