A dense plasma focus device can produce dense and high energy plasma in a short time. Recently, it has been proposed that the device could be applied to fusion for clean energy production (focus fusion). In order to understand the behavior of the plasma current filaments in the device, two-dimensional, relativistic, fully electromagnetic, particle-in-cell simulations were performed. Sixteen plasma current filaments were initially located on the edge of a circle in our model. They begin to interact with each other while pinching, and then coalesce in the vicinity of the center of system. In the pinch phase (during the coalescence), there appears dense plasma, whose maximum number density is 10 times larger than the initial value. The ions are accelerated, but the rate of the number of them is somewhat small. After that, the current becomes unstable and jumps out from the center. These results are useful for understanding the coalescence process of current filaments.