As machine learning (ML) application continues to expand across diverse fields, there is a rising demand for ML code generation. In this paper, we aim at a critical research question: Can machines autonomously generate ML code for sophisticated, human-designed algorithms or solutions? To answer this question, we introduce a novel benchmark, MLAlgo-Bench, which includes two challenging tasks: 1) Generating code for ML algorithms including both traditional ML and modern deep learning-based methods, and 2) Giving humans solution sketches, writing ML code for solving practical tasks in Kaggle competitions. This benchmark is unique in its focus on the challenges of interpreting intricate human instructions and producing multi-step, high-complexity code, offering a rigorous test for current Large Language Model (LLM) capabilities. We introduce an automatic evaluation framework with comprehensive metrics such as task pass rate, relative performance metric, and time overhead. Currently, the top-performing models (Claude3.5-Sonet) achieve a 48.8% task completion rate on realizing machine learning algorithms, and a 21.6% rate for completing Kaggle competitions. Further analysis suggests substantial room for improvement.