This study develops a duopoly model with quality and price competition, and investigates the corporate demand for insurance. Our model predicts asymmetric strategic effects of insurance for two firms with different qualities, because the increases in the quality of each firm have opposite effects on the intensity of price competition. We show that lowquality firm has positive strategic effect of insurance, and might purchase insurance, whereas high-quality firm has negative strategic effect of insurance and never purchases insurance if firms are risk-neutral. When firms are risk-averse, however, high-quality firm might also purchase insurance if the cost of risk is sufficiently large, so that the benefit of insurance exceeds the sum of the strategic effect and the cost of insurance. We show that the availability of insurance might raise the quality levels of both firms.