A　positive-definite　homogeneous　multivariate　form　plays　a　critical　role　in　the　medical　imaging　and　automatic　control,　and　the　definiteness　of　this　form　can　be　identified　by　a　special　structure　tensor.　In　this　paper,　we　first　state　the　equivalence　between　the　positive-definite　multivariate　form　and　the　corresponding　tensor　and　account　for　the　links　between　the　positive-definite　tensor　with　a　strong　H-tensor.　Then　based　on　weak　reducibility,　some　criteria　were　provided　to　identify　strong　H-tensors.　Furthermore,　with　these　relations,　we　establish　an　iterative　scheme　to　identify　the　positive-definite　multivariate　homogeneous　form　and　prove　it　is　theoretically　valid.　Numerical　experiments　were　given　to　illustrate　the　practicality　of　the　scheme.