We report complex metamagnetic transitions in single crystals of the new low carrier Kondo antiferromagnet YbRh3Si7. Electrical transport, magnetization, and specific heat measurements reveal antiferromagnetic order at TN=7.5 K. Neutron diffraction measurements show that the magnetic ground state of YbRh3Si7 is a collinear antiferromagnet, where the moments are aligned in the ab plane. With such an ordered state, no metamagnetic transitions are expected when a magnetic field is applied along the c axis. It is therefore surprising that high-field magnetization, torque, and resistivity measurements with H∥c reveal two metamagnetic transitions at μ0H1=6.7 T and μ0H2=21 T. When the field is tilted away from the c axis, towards the ab plane, both metamagnetic transitions are shifted to higher fields. The first metamagnetic transition leads to an abrupt increase in the electrical resistivity, while the second transition is accompanied by a dramatic reduction in the electrical resistivity. Thus, the magnetic and electronic degrees of freedom in YbRh3Si7 are strongly coupled. We discuss the origin of the anomalous metamagnetism and conclude that it is related to competition between crystal electric-field anisotropy and anisotropic exchange interactions.