For any given finite p-group G, we will construct a number field F of finite degree such that the Galois group of the maximal unramified p-extension over F is isomorphic to G; this can be regarded as an extension of the construction of number fields of finite degree with prescribed p-part of the class group, which was done by Yahagi in 1978. As a consequence of this construction, we will find that any pro-p-group with countably many generators must occur in the Galois groups of maximal unramified p-extensions of number fields (not necessary finite degree).