Summary: We develop a reduced-form credit risk model with regime-switching intensities to investigate the pricing of a credit default swap (CDS) contract. We assume that the defaults of all the names are driven by some shock events. The arrivals of the shock events and the interest rate are modelled by a multivariate regime-switching shot noise process. We provide the flexibility that the model parameters, including the intensities and the jump sizes of the jump component, can switch over time according to a continuous-time, finite-state Markov chain. The states of the chain may be interpreted as different states of an economy or different stages of a business cycle. Based on the joint Laplace transform of the regime-switching shot noise processes, we derive the explicit formulas for the spreads of CDS contract with and without counterparty risk. Numerical results illustrate changes of market regimes have a significant effect on the spread.