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In this paper, we propose an enhanced direction-of-arrival (DOA) estimation method using linearly predicted array expansion to improve the angular resolution for automotive radar systems with a small number of antenna elements. The proposed method extracts the linear relation among signals received in the array antenna and uses it to generate extrapolated signals outside the array antenna. Finally, we apply the DOA estimation methods, such as the Bartlett and multiple signal classification algorithms, to both the original and extrapolated signals, and verify its performance through simulations and field experiments. From the simulation results, in terms of root-mean-square error and resolution probability, we observed that the proposed method had a higher angular resolution and estimation accuracy than conventional interpolation and extrapolation methods. Moreover, with the experiment results, we verified that the proposed array expansion method can be suitably applied to commercial automotive radar systems.