This paper considers a Gaussian multiple-input single-output (MISO) broadcast channel with a per-antenna peak power constraint (or simply peak power constraint). It is more realistic to consider the peak power constraint on each transmit antenna because in many practical implementations each antenna is equipped with its own power amplifier. Assuming the perfect knowledge of the channel state information (CSI) at the transmitter, we propose an achievable scheme using dirty-tape coding (DTC). The ideal dirty-paper coding (DPC), which is a capacity-achieving scheme for the Gaussian multiple-input multiple-output (MIMO) broadcast channel, cannot be used for our model because its optimal input distribution is Gaussian and thus the peak power constraint is violated. On the other hand, the channel input of DTC is uniformly distributed in a fixed range, which helps to control the peak power of the transmit signal easily. We also present an algorithm that finds capacity-achieving beamforming vectors and power allocation factors under a per-antenna average power constraint and use the optimized parameters in the proposed scheme. Simulation results show that the proposed scheme provides gains of 2.7dB over a non-DTC scheme based on minimum mean square error (MMSE) beamforming at high signal-to-noise ratio (SNR) when there are three receivers and the transmitter has three antennas.