With the continuous development of terahertz (THz) technology in recent years, many kinds of THz functional devices including switchers, filters, modulators, isolator and polarizers have been demonstrated. However, researches of the focusing devices in the terahertz frequency range are rarely reported. In this paper, we propose a subwavelength metal-air-InSb-metal periodic array structure to perform terahertz wave focusing. The dependence of permittivity of InSb in the THz regime on external magnetic field and temperature is calculated theoretically. Based on the magneto-optical effect of the semiconductor material InSb and asymmetrical waveguide structure, the influences of external magnetic field and temperature on the focusing and transmittance characteristics of the device are studied in detail. Numerically simulated results show that the structure proposed above can not only improve the transmittance greatly but also perform focusing perfectly. Calculations on the transmission properties show that in a certain range of temperature, the power flow transmittance at the focus point increases with the increase of temperature. In the meantime, for a certain temperature, with increasing the external magnetic field, the power flow continuously increases as well and reaches a maximum value at a certain magnetic field. For example, for a temperature of 172 K and a magnetic field of 0.6 T, the maximum power flow transmitted at the focus point is 10200 W/m2 at 0.8 THz, which is about 28 times larger than that without magnetic field at the same temperature. In addition, the simulation results also show that when the temperature and external magnetic field are fixed at 172 K and 0.5 T, respectively, the power flow transmittances for the incident waves at different frequencies are different. There is a peak value of the transmittance appearing at a specific frequency of 0.8 THz. Moreover, when the incident wave frequency is far from 0.8 THz, the transmittance decreases dramatically. It is worth noting that by choosing different temperatures and external magnetic fields, the structure proposed can not only enhance the transmittance over 20 times at the focus point, but also manipulate effectively the THz wave in a broad operating bandwidth of 400 GHz from 0.4 THz to 0.8 THz. These properties indicate that the proposed structure can act as an ideal tunable, broadband, and high transmittance focusing device in the terahertz regime.