Since the lattice Boltzmann method (LBM) originally carries out the simulations on the regular Cartesian lattices; curved boundaries are often approximated as a series of stair steps. The most commonly employed technique for resolving curved boundary problems is extrapolation of macroscopic properties at boundary nodes. Previous investigations have indicated that using more than one equation for extrapolation in boundary condition potentially causes abrupt changes in particle distributions. Therefore, a new curved boundary treatment is introduced to improve computational accuracy of the conventional stair-shaped approximation used in lattice Boltzmann simulations by using a unified equation for extrapolation of macroscopic variables. This boundary condition is not limited to fluid flow and can be extended to other physical fields. The proposed treatment is tested against several well established problems. Numerical results show that the present treatment is of second-order accuracy, and has well-behaved stability characteristics.