Abstract: Category of L-subinclines and its properties are studied.Firstly,the category of L-subinclines L-SInc is defined, and it is proved to be a topological category on the category of inclines,the formation of equalizer and product in L-SInc are given,and it is proved that the category L-SInc has pull back.Secondly,the consept of L-cotower of inclines and the category of them are defined, it is proved that,the category L-SInc and category IncCL are isomorphic under some appropriate condition.