This paper focuses on a linear quadratic non-zero sum differential game problem derived by backward stochastic differential equation with asymmetric information, which is a natural continuation of Wang and Yu [IEEE TAC (2010) 55: 1742-1747, Automatica (2012) 48: 342-352]. Different from Wang and Yu [IEEE TAC (2010) 55: 1742-1747, Automatica (2012) 48: 342-352], novel motivations for studying this kind of game are provided first. Then some feedback Nash equilibrium points are uniquely obtained by forward-backward stochastic differential equations, their filters and the corresponding Riccati equations.