It has been shown that normal cyclic movement of human arm and resting limb tremor in Parkinson's disease (PD) are associated with the oscillatory neuronal activities in different cerebral networks, which are transmitted to the antagonistic muscles via the same spinal pathway. There are mono-synaptic and multi-synaptic corticospinal pathways for conveying motor commands. This study investigates the plausible role of propriospinal neuronal (PN) network in the C3–C4 levels in multi-synaptic transmission of cortical commands for oscillatory movements. A PN network model is constructed based on known neurophysiological connections, and is hypothesized to achieve the conversion of cortical oscillations into alternating antagonistic muscle bursts. Simulations performed with a virtual arm (VA) model indicate that without the PN network, the alternating bursts of antagonistic muscle EMG could not be reliably generated, whereas with the PN network, the alternating pattern of bursts were naturally displayed in the three pairs of antagonist muscles. Thus, it is suggested that oscillations in the primary motor cortex (M1) of single and double tremor frequencies are processed at the PN network to compute the alternating burst pattern in the flexor and extensor muscles.