Taking into account the self-weight load is crucial for designing large-scale truss structures. However, the self weight of a truss has been often ignored in Structural optimization, because of the difficulty stemming from its dependency on the truss design which itself is to be optimized. This paper presents a mixed-integer second-order cone programming approach to truss topology optimization under the self-weight load and the upper bound constraint on the number of nodes. The latter constraint is practically significant from the viewpoint of fabrication cost. It is also illustrated through the numerical experiments that the constraint on the number of nodes often yields a simple truss design, which is preferable from the viewpoint of manufacturability.