A new two-dimensional interface reconstruction method that ensures continuity of the interface and preserves volume fractions is presented here. It is made of two steps, first, the minimization of a cost functional based on volume fractions least square errors by using dynamic programming, a fast and efficient scheme well known in image processing, and then a local correction phase. In each cell, the interface is made of two line segments joining two edges. This new interface reconstruction method, called Dynamic Programming Interface Reconstruction has been coupled with various advection schemes, among them the Lagrange + remap scheme. With a reasonable computational cost, it has been observed in various test cases that Dynamic Programming Interface Reconstruction is more accurate and less diffusive compared with other existing classical reconstruction methods. Copyright (C) 2017 John Wiley and Sons, Ltd.