The energy spectrum and alpha-spectroscopic factors of Ca-40 are calculated by using an alpha + Ar-36 orthogonality condition model. Overall agreement is obtained with the experimental data. The model successfully produces the parity-doublet K-pi = 0(+) and 0(-) alpha + Ar-36 cluster bands. It is shown that the coexistence and interference of alpha-cluster states and shell-model states are indispensable to understand the structure of Ca-40.