A　square　matrix　over　a　semiring　is　called　strongly　invertible　if　all　of　its　leading　principal　submatrices　are　invertible.　In　this　paper,　the　strongly　invertible　matrices　over　a　semiring　are　discussed　and　an　equivalent　condition　for　a　square　matrix　over　a　semiring　to　be　strongly　invertible　is　given.　Also,　some　equivalent　descriptions　are　obtained　for　a　semiring　over　which　the　product　of　any　two　strongly　invertible　matrices　with　the　same　size　is　strongly　invertible.　Some　of　the　results　obtained　in　this　paper　generalize　and　develop　previous　results　for　matrices　over　the　field　of　complex　numbers　and　matrices　over　commutative　rings.　©　2017,　©　2017　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.