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This work proposes a new direction-of-arrival (DOA) estimation algorithm for directional antenna arrays. Most of the existing DOA algorithms are difficult to work with directional antenna arrays due to the characters of directional elements and thus proper modification is required. The proposed algorithm is based on Capon algorithm through the introduction of a new optimisation problem, which aims to maintain the array gain in the `look direction', so that the DOA can be estimated correctly using a directional antenna array. To verify the performance of the proposed algorithm, computer simulations are performed and then the results obtained are compared with the Capon algorithm. The results show that the proposed algorithm outperforms the Capon algorithm.