For analytic self-maps φ of the unit disk, we develop a necessary and sufficient condition for the composition operator Cφ to be closed-range on the classical Bergman space $\mathbb{A}^{2}$ . This condition is relatively easy to apply. Particular attention is given to the case that φ is an inner function. Included are observations concerning angular derivatives of Blaschke products. In the case that φ is univalent, it is shown that Cφ is closed-range on $\mathbb{A}^{2}$ only if φ is an automorphism of the disk.