Various correlations in system of single Jaynes-Cummings (J-C) atom and an isolated atom were investigated via the measurement of geometric quantum discord proposed by Dakic et al. The dynamical evolutions of geometric quantum discord between two atoms were numerically analyzed as well as those of the quantum entanglement and quantum discord. Results show that quantum correlations can be increased by increasing initial entanglement and purity of the prepared W-state of the two atoms. The coupling constant and photon number play significant roles in the quantum correlation dynamics.