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With the development of society, there is an increasingly urgent demand for light-weight, high-strength, and high-temperature-resistant structural materials. High-entropy alloys (HEAs) owe much of their unusual properties to the selection among three phases: solid solution (SS), intermetallic compound (IM), and mixed SS and IM (SS and IM). Therefore, accurate phase prediction is crucial for guiding the selection of element combinations to form HEAs with desired properties. Light high-entropy alloys (LHEAs), as a significant branch of HEAs, exhibit excellent performance in terms of specific strength. In this study, we employ a machine learning (ML) method to realize the design of light-weight high-entropy alloys based on solid solutions. We determined the Gradient Boosting Classifier model as the best machine learning model through a two-step feature and model selection, in which its accuracy and F1_Score achieve 0.9166 and 0.8923. According to the predicted results, we obtained Al₂₈Li₃₅Mg₁₅Zn₁₀Cu₁₂ LHEAs, which are mainly composed of 90% solid solution. This alloy accords with the prediction results of machine learning. But it is made up of a two-phase solid solution. In order to obtain a light-weight high-entropy alloy dominated by a single solid solution, we designed Al₂₄Li₁₅Mg₂₆Zn₉Cu₂₆ LHEAs on the basis of machine learning prediction results accompanied by expert experience. Its main structure includes a single-phase solid solution. Our work provides an alternative approach to the computational design of HEAs and provides a direction for future exploration of light-weight high-entropy alloys.