To investigate the ignition process in a diesel spray, the ignition in a transient fuel spray is analyzed numerically by a discrete droplet spray model (DDM) coupled with the Shell kinetics model at various operating conditions. Predicted results show that the fuel mixture injected at the start of injection, which travels along midway between the spray axis and the spray periphery, contributes heavily to the first ignition in a spray. The equivalence ratio and temperature of the first ignited mixture are kept nearly constant until the start of hot ignition. The temperature of the first ignited mixture is kept at a constant value of higher temperature than the thermodynamic equilibrium temperature of the mixture before the hot ignition starts. The equivalence ratio of the first ignited mixture is around 1.6 at initial gas temperatures between 750 K and 850 K. When the initial gas temperature increases from 850 K to 1000 K, this equivalence ratio increases up to 2.5 through the effect of negative temperature coefficient region (NTC).