We report electrical resistivity on a single crystal of the hole-doped two-leg ladder compound Sr2Ca12Cu24O41, which becomes superconducting with T(c)similar to 5 K only at pressures above similar to 3.0 GPa. Measurements were performed at nearly hydrostatic pressures up to 5.7 GPa and low temperatures down to 100 mK under static magnetic fields up to 20 T parallel to the a axis (along the ladder rungs) and up to 7 T parallel to both the b axis (perpendicular to the ladder plane) and the c axis (along the ladder legs). A clear difference in the resistive upper critical field H-c2(T) is observed among these three directions, confirming that this system has a highly anisotropic superconducting ground state. Also, H-c2(T) parallel to the ladder plane is found to exceed the Pauli limit by a factor of more than 2, suggesting either a strong spin-orbit scattering or spin-triplet pairing. Furthermore, it is implied, from measurements of resistivity versus angle of magnetic field in the bc plane, that another superconducting phase is stable below around 3 K only when the magnetic field is applied exactly along a certain direction that is +/- 35 degrees from the ladder direction.