<p>The Behrens–Fisher problem is a fundamental and important problem in applied statistics. Among the existing approaches, the commonly used Welch's approximate <i>t</i> test has the greatest powers in most cases; however, Welch's <i>t</i> test may be liberal for small sample sizes. As three modified approaches, the GPQ, CC and MIM tests are conservative in controlling Type I risk. In this paper, a new test based on the inferential model (IM) framework is proposed to deal with Behrens–Fisher problem. Simulation studies show that the IM test is very easy to operate and does improve the GPQ, CC and MIM tests in terms of both Type I error rates and statistical powers. Moreover, the powers of our IM test are close to those of Welch's <i>t</i> test. In this sense, our IM test can be a competitive alternative method to the <i>t</i> test. More importantly, unlike the classical solution, the IM's output is posterior-probabilistic in nature and, therefore, has a meaningful interpretation within and not just across experiments. Finally, a real example is used to demonstrate the application of the proposed method.</p>