The quantum mechanical second virial coefficient of a gas with square-well plus hard-core potential is evaluated at low and high temperatures. The low temperature result is given in a series in the ascending powers of (α/λ), and the first four oefficients are given. The direct part of the second virial coefficient at high temperature is given in a series in the ascending powers of (λ/α), and the first three coefficients are given. Our result for the first coefficient in the high temperature series is in agreement with the result of previous workers. Copyright © 1977 American Institute of Physics.