This article aims to investigate the curvature operator of the second kind on Kähler manifolds. The first result states that an m-dimensional Kähler manifold with $$\frac{3}{2}(m^2-1)$$-nonnegative (respectively, $$\frac{3}{2}(m^2-1)$$-nonpositive) curvature operator of the second kind must have constant nonnegative (respectively, nonpositive) holomorphic sectional curvature. The second result asserts that a closed m-dimensional Kähler manifold with $$\left( \frac{3m^3-m+2}{2m}\right) $$-positive curvature operator of the second kind has positive orthogonal bisectional curvature, thus being biholomorphic to $${{\mathbb {C}}}{{\mathbb {P}}}^m$$. We also prove that $$\left( \frac{3m^3+2m^2-3m-2}{2m}\right) $$-positive curvature operator of the second kind implies positive orthogonal Ricci curvature. Our approach is pointwise and algebraic.