The ordering of polar hydrogen bonds may break space inversion symmetry and induce ferroelectricity or antiferroelectricity. This process is usually immune to external magnetic fields so that magnetic control of hydrogen bonds is very challenging. Here we demonstrate that the ordering of hydrogen bonds in the metal-organic frameworks [(CH_{3})_{2}NH_{2}]M(HCOO)_{3} (M=Fe, Co) can be manipulated by applying magnetic fields. After cooling in a high magnetic field, the order-disorder transition of hydrogen bonds shifts to a lower or higher temperature, depending on antiferroelectricity or ferroelectricity induced by hydrogen bond ordering. Besides, the order-disorder transition leads to a giant thermal expansion, exceeding ∼3.5×10^{4} and ∼2×10^{4} ppm for M=Fe and Co, respectively, which is much higher than that of inorganic ferroelectrics. The influence of magnetic field on hydrogen bond ordering is discussed in terms of the magnetoelastic coupling.