Conventionally, the energy band theory is used to explain the magnetic and electrical transport properties of metals. However, so far, there has been no quantitative explanation of the relations between the average magnetic moment per atom and the resistivity for Fe, nor Ni, nor Co metals. In this paper, a new itinerant electron model for magnetic metal is proposed on the basis of electron distribution theory at the energy level. 1) In the process of free atoms forming the metal solid, most of the 4s electrons of Fe, Ni and Co enter into the 3d orbits subjected to the Pauli repulsive force, and the remaining 4s electrons form free electrons. 2) Since the average number of 3d electrons is not an integer, a part of atoms have one 3d electron more than the other atoms. These excess 3d electrons have a certain probability to itinerate between the 3d orbits of the adjacent atoms as itinerant electrons; and the other 3d electrons are local electrons. 3) The transition probability of itinerant electrons is very low, thus the contribution to metal resistivity from itinerant electrons is far lower than that from free electrons. Resistivity of metal decreases with increasing the number of free electrons. Therefore, using the observed values of average atomic magnetic moments, 2.22, 0.62 and 1.72 B, the average numbers of free electrons in Fe, Ni and Co can be calculated to be 0.22, 0.62 and 0.72, respectively. This is the reason why the electrical resistivities of Fe, Ni and Co (8.6, 6.14 and 5.57 -cm) decease successively. In addition, according to this model, the average number of 3d electrons per atom in Ni metal is 9.38. This indicates that 38% of atoms in Ni metal have ten 3d electrons, forming a full 3d sub-shell, as in Cu or Zn atoms. The 3d electrons in these atoms are difficult to itinerate or exchange. This may be the reason why the Curie temperature of Ni metal (631 K) is far lower than those of Fe and Co metals (1043 and 1404 K). On the basis of the energy band theory, the numbers of 3d electrons in Fe, Ni and Co metals are 7.4, 9.4 and 8.3, which are close to our results (7.78, 9.38 and 8.28), respectively. This indicates that our model is consistent with the energy band theory. Compared with the complex energy band theory, a simple and effective method on investigating valence electron structures through the experimental average magnetic moments per atom in a metal is presented based on our model. Therefore, the new itinerant electron model may be a new clue to understanding the electronic structure of metals and alloys.