The wave functions, energy levels and matrix elements of Yb+ ions are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined. Then, the magic wavelengths of the magnetic sublevel 6s
1/2, m=1/2 → 5d
3/2, m=±3/2, ±1/2 and 6s
1/2, m=1/2→ 5d
5/2, m=±5/2, ±3/2, ±1/2 transitions in the linearly, right-handed and left-handed polarized light are further determined. The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.