Semantic communication is recognized for its high compression efficiency and robust resistance to noise. However, utilizing a fixed transmission rate in environments with dynamic signal-to-noise ratios (SNR) often results in inefficient use of communication resources. To address this challenge, this letter proposes an importance-aware rate control semantic communication (IRCSC) scheme, which dynamically adjusts transmission rates in response to both channel conditions and semantic importance. The scheme employs a contribution-based importance analyzer to rank semantic importance. Additionaly, a novel metric, the semantic transmission integrity index (STII), is proposed to quantify the amount of correctly transmitted information and to correlate it with inference performance. Simulations indicate that, with low computational complexity, IRCSC guarantees a controllable trade-off between performance and rate, delivering higher compression efficiency and improved task performance in high-SNR scenarios.