The origin of low α/Fe ratios in some metal-poor stars, the so-called low-α stars, is discussed. It is found that most of low-α stars in the Galaxy are on the main sequence. This strongly suggests that these stars suffered from external pollution. It is also found that the Zn/Fe abundance ratios of low-α stars both in the Galaxy and in dwarf spheroidal galaxies are lower than the average value of Galactic halo stars, whereas damped Lyα absorbers have higher ratios. This implies that some low-α stars accreted matter that was depleted from gas onto dust grains. To explain the features in these low-α stars, we have proposed that metal-poor stars harboring planetary systems are the origin of these low-α stars. Stars engulfing a small fraction of planetesimals enhance the surface content of Fe to exhibit low α/Fe ratios on their surfaces, while they are on the main sequence, because dwarfs have shallow surface convection zones where the engulfed matter is mixed. After the stars leave the main sequence, the surface convection zones become deeper, reducing the enhancement of Fe. Eventually, when the stars ascend to the tip of the red giant branch, they engulf giant planets to become low-α stars again as observed in dwarf spheroidal galaxies. We predict that low-α stars with low Mn/Fe ratios harbor planetary systems.