<p>We propose an immersed boundary method (IBM) with a curvature-dependent, area-preserving correction algorithm for binary immiscible incompressible fluid flows. The IBM was first proposed to solve biofluid dynamics in complex geometries, and researchers later used it for multiphase fluid flows due to its direct and simple representation of complex interfaces. In this method, two types of grids are needed: an Eulerian formulation for the computation of fluid flow and a Lagrangian representation for the movement of the immersed boundary. If the conventional method is used, area loss or area increases occur due to numerical discretization errors. In the proposed correction method, the positions of the Lagrangian interface points are adjusted along the normal direction in proportion to the local curvature. Numerical examples of droplet deformation under various flow conditions show that the proposed algorithm can discretely preserve the initial area while the interface undergoes large deformation.</p>