This paper focuses on a kind of LQ non-zero sum differential game driven by backward stochastic differential equation with asymmetric information, which is a natural continuation of Wang and Yu (2010), Wang and Yu (2012). Different from Wang and Yu (2010) and Wang and Yu (2012), a realistic motivation for studying this kind of game is provided, and some feedback Nash equilibrium points are uniquely obtained by forward-backward stochastic differential equations, their filters and the corresponding Riccati equations with Markovian setting. (C) 2018 Elsevier Ltd. All rights reserved.