Atmospheric pressure plasma jet (APPJ) has attracted much attention due to its versatile applications in various fields, which normally operates in either a guided-streamer mode or a continuous-discharge mode. In this paper, temporal evolution is observed from the guided-streamer mode to the continuous-discharge one in an argon APPJ excited by a sinusoidal voltage. Waveforms of voltage and current indicate that the voltage applied to the electrode is distorted severely from the ideal sine. For the guided-streamer mode, there is only one discharge pulse per half voltage cycle. For the mode transition or the continuous-discharge mode, there is only one discharge composed of a pulse and a hump per half voltage cycle. Fast photography implemented for the mode transition reveals that both the discharges in the positive and the negative voltage polarities evolve from the guided-streamer mode to the continuous-discharge one. In the guided-streamer mode of the mode transition, the discharge behaves as a positive streamer in the positive voltage polarity, while a negative streamer in the negative voltage polarity. In addition, the mode transition only occurs in a range of dissipated power and gap width. Based on optical emission spectroscopy, temporal evolutions of the mode transition are investigated for excited electron temperature, electron density, and field strength. Moreover, their spatial distributions along the argon stream are studied at different time instants. These results are of great importance for the discharge dynamics of APPJ.