We investigate the collection behaviour of coupled phase oscillators on Newman- Watts small-world networks in one and two dimensions. Each component of the network is assumed as an oscillator and each interacts with the others following the Kuramoto model. We then study the onset of global synchronization of phases and frequencies based on dynamic simulations and finite-size scah g. Both the phase and frequency synchronization are observed to emerge in the presence of a tiny fraction of shortcuts and enhanced with the increases of nearest neighbours and lattice dimensions.