Abstract: An image interpolation method with gradient angle constraints is proposed to obtain smooth image contours and crisp edges．First, awe have proved that the constraint of local constant gradient angles is equivalent to the minimization of total variation．Based on this, aa stronger continuity constraint of gradient angle is presented．The interpolation formula （a3-degree-PDE） derived from the constraint can ensure the continuity of level lines and reduce the width of edges．The contrast invariant of the regularizer of the formula is also proved．Numerical experiments demonstrate the validity of the proposed algorithm．