We studied the magnetic and magnetoelectric properties of Ba2-xSrxNi2Fe12O22 single crystals over a wide composition range (0 ≤ x ≤ 1.5). All the crystals show a ferrimagnetic order at around 660 K. While a Sr-free crystal is simply ferrimagnetic down to the lowest temperature, a transition from the ferrimagnetic into a screw magnetic ordered state was observed at temperatures below 300 K in Sr-substituted crystals. The transition temperature monotonically increases with increasing Sr content, meaning that the screw ordered state is stabilized by the Sr-substitution. By applying a magnetic field perpendicular to the hexagonal c axis, the samples showing the ground-state screw order undergo successive metamagnetic transitions and exhibit magnetically induced ferroelectricity in some of the intermediate magnetic phases. In an intermediate magnetic phase, the largest electric polarization emerges (2 × 102 μC/m2 for x = 1.5 crystal), i.e., magnetoelectric effect. The evolution of the magnetic structures related to the magnetoelectric effect in x = 1.5 crystal was clarified by means of in-field neutron diffraction measurements. Though the magnetoelectric effect in the as-grown crystal was measurable only below ∼100 K due to its low resistivity, a post-annealing drastically enhances the resistivity and allows us to observe the magnetically induced ferroelectricity up to ∼175 K.