When the solar wind interacts with the ionosphere of an unmagnetized planet, it induces currents that form an induced magnetosphere. These currents and their associated magnetic fields play a pivotal role in controlling the movement of charged particles, which is essential for understanding the escape of planetary ions. Unlike the well-documented magnetospheric current systems, the ionospheric current systems driven by solar wind and atmospheric neutral winds have not been quantitatively observed, which constrains the quantification of energy transfer from stars to these planets. Here, utilizing eight years of data from the Mars Atmosphere and Volatile EvolutioN (MAVEN) mission, we investigate the global distribution of ionospheric currents on Mars. We identify two distinct current systems in the ionosphere: one aligns with the solar wind electric field but exhibits hemispheric asymmetry perpendicular to the solar wind electric field direction; the other corresponds to the flow pattern of annually averaged neutral winds. We propose that these two current systems are driven by the solar wind and atmospheric neutral winds, respectively. Our findings reveal that Martian ionospheric dynamics are influenced by the neutral winds from below and the solar wind from above, highlighting the complex and intriguing nature of current systems on unmagnetized planets.