It is difficult to extract feature points in the underwater environment owing to light refraction and water turbidity. To solve this problem, an underwater binocular measurement system that detects visual features using a line-structured light array is designed in this study. A large number of feature points are obtained by extracting the center of light strip. The refraction model of the underwater binocular's optical path is established, and an improved epipolar matching method is proposed to obtain the three-dimensional coordinates of feature points to realize the measurement and the restoration of three-dimensional morphology of underwater objects. The experimental results show that the measurement accuracy of the proposed method for underwater objects is comparable to that for land, and the measurement error is within 0.3 mm, which meets the measurement accuracy requirements. The measurement process of the proposed system is fast and accurate, and it is suitable for underwater real-time positioning measurement.