Regression and variable selection in high-dimensional settings, especially when $p\gg n$ has been a popular research topic in statistical machine learning. In recent years, many successful methods have been developed to tackle this problem. In this paper, we propose the multi-step adaptive elastic-net (MSA-Enet), a multi-step estimation algorithm built upon adaptive elastic-net regularization. The numerical study on simulation data and real-world biological data sets have shown that the MSA-Enet method tends to significantly reduce the number of false-positive variables, while still maintain the estimation accuracy. By analysing the variables eliminated in each step, more insight could be gained about the structure of the correlated variable groups. These properties are desirable in many real-world variable selection and regression problems.