An inbred corn variety, designated LH351, is disclosed. The invention relates to the seeds of inbred corn variety LH351, to the plants of inbred corn variety LH351 and to methods for producing a corn plant, either inbred or hybrid, by crossing the inbred variety LH351 with itself or another corn variety. The invention further relates to methods for producing a corn plant containing in its genetic material one or more transgenes and to the transgenic plants produced by that method and to methods for producing other inbred corn varieties derived from the inbred LH351.