A nickel hydrogen rechargeable battery in which an electrode group is airtightly contained in a container together with alkaline electrolyte, and the electrode group is formed of a separator, a negative electrode and a positive electrode, characterized in that: the negative electrode includes: hydrogen storage alloy having a composition indicated by a general formula Ln 1-w Mg w Ni x Al y T z, wherein Ln represents at least one element selected from lanthanoid, Ca, Sr, Sc, Y, Ti, Zr and Hf; T represents at least one element selected from V, Nb, Ta, Cr, Mo, Mn, Fe, Co, Ga, Zn, Sn, In, Cu, Si, P and B; and subscripts w, x, y and z represent 0<w ≤1, 2.80≤x≤3.50, 0.10≤ y≤ 0.25, and 0≤ z≤ 0.5, respectively; the positive electrode contains: positive-electrode active material including nickel hydroxide in which magnesium is dissolved; at least either one of the negative electrode and the positive electrode further contains as additive (38, 46) at least one selected from a group including zinc and zinc compounds; the content of the additive (38, 46): ranges from 0.2 to 1.5 part by weight per 100 parts by weight of the hydrogen storage alloy in the negative electrode, and ranges from 0.3 to 1.5 part by weight per 100 parts by weight of the positive-electrode active material in the positive electrode. the negative electrode includes: hydrogen storage alloy having a composition indicated by a general formula Ln 1-w Mg w Ni x Al y T z, wherein Ln represents at least one element selected from lanthanoid, Ca, Sr, Sc, Y, Ti, Zr and Hf; T represents at least one element selected from V, Nb, Ta, Cr, Mo, Mn, Fe, Co, Ga, Zn, Sn, In, Cu, Si, P and B; and subscripts w, x, y and z represent 0<w ≤1, 2.80≤x≤3.50, 0.10≤ y≤ 0.25, and 0≤ z≤ 0.5, respectively; hydrogen storage alloy having a composition indicated by a general formula Ln 1-w Mg w Ni x Al y T z, wherein Ln represents at least one element selected from lanthanoid, Ca, Sr, Sc, Y, Ti, Zr and Hf; T represents at least one element selected from V, Nb, Ta, Cr, Mo, Mn, Fe, Co, Ga, Zn, Sn, In, Cu, Si, P and B; and subscripts w, x, y and z represent 0<w ≤1, 2.80≤x≤3.50, 0.10≤ y≤ 0.25, and 0≤ z≤ 0.5, respectively; the positive electrode contains: positive-electrode active material including nickel hydroxide in which magnesium is dissolved; at least either one of the negative electrode and the positive electrode further contains as additive (38, 46) at least one selected from a group including zinc and zinc compounds; positive-electrode active material including nickel hydroxide in which magnesium is dissolved; at least either one of the negative electrode and the positive electrode further contains as additive (38, 46) at least one selected from a group including zinc and zinc compounds; the content of the additive (38, 46): ranges from 0.2 to 1.5 part by weight per 100 parts by weight of the hydrogen storage alloy in the negative electrode, and ranges from 0.3 to 1.5 part by weight per 100 parts by weight of the positive-electrode active material in the positive electrode. ranges from 0.2 to 1.5 part by weight per 100 parts by weight of the hydrogen storage alloy in the negative electrode, and ranges from 0.3 to 1.5 part by weight per 100 parts by weight of the positive-electrode active material in the positive electrode.