The strong performance of large language models (LLMs) raises extensive discussion on their application to code generation. Recent research suggests continuous program refinements through visible tests to improve code generation accuracy in LLMs. However, these methods suffer from LLMs' inefficiency and limited reasoning capacity. In this work, we propose an LLM programming workflow (LPW) designed to improve both initial code generation and subsequent refinements within a structured two-phase workflow. Specifically, the solution generation phase formulates a solution plan, which is then verified through visible tests to specify the intended natural language solution. Subsequently, the code implementation phase drafts an initial code according to the solution plan and its verification. If the generated code fails the visible tests, the plan verification serves as the intended solution to consistently inform the refinement process for correcting bugs. Compared to state-of-the-art methods across various existing LLMs, LPW significantly improves the Pass@1 accuracy by up to 16.4% on well-established text-to-code generation benchmarks. LPW also sets new state-of-the-art Pass@1 accuracy, achieving 98.2% on HumanEval, 84.8% on MBPP, 59.3% on LiveCode, 62.6% on APPS, and 34.7% on CodeContest, using GPT-4o as the backbone. Our code is publicly available at: https://github.com/you68681/lpw