A cowpea cultivar designated 95-104 is disclosed. The invention relates to the seeds of cowpea cultivar 95-104, to the plants of cowpea cultivar 95-104, to plant parts of cowpea cultivar 95-104 and to methods for producing a cowpea plant produced by crossing cowpea cultivar 95-104 with itself or with another cowpea cultivar. The invention also relates to methods for producing a cowpea plant containing in its genetic material one or more transgenes and to the transgenic cowpea plants and plant parts produced by those methods. This invention also relates to cowpea cultivars or breeding cultivars and plant parts derived from cowpea cultivar 95-104, to methods for producing other cowpea cultivars, lines or plant parts derived from cowpea cultivar 95-104 and to the cowpea plants, varieties, and their parts derived from use of those methods. The invention further relates to hybrid cowpea seeds, plants and plant parts produced by crossing the cowpea cultivar 95-104 with another cowpea cultivar.