This research proposes a new algorithm called Linear-Complexity Multiplication (L-Mul) to approximate floating-point multiplication using integer addition operations. L-Mul reduces energy consumption by significantly reducing the computation resources needed for neural network inference, particularly in large language models (LLMs). The paper analyzes the theoretical error expectation of L-Mul and demonstrates its effectiveness through numerical experiments on various tasks, including language understanding, reasoning, and visual question answering. The authors evaluate L-Mul's performance against different precision settings and show that it achieves comparable or even higher accuracy than 8-bit floating-point multiplications while requiring less computational power, making it a promising method for energy-efficient AI model deployment.