<p>We investigate a two-player non-zero-sum linear-quadratic stochastic differential game under asymmetric information, where the state dynamics is governed by a jump diffusion. The asymmetry in information stems from the structure of the players’ strategies: while one player makes decisions based on full information, the other operates under delayed information due to a time delay in his/her control input. Using the maximum principles and the orthogonal decomposition and reorganization technique, we transform the problem of finding open-loop Nash equilibria to that of solving an auxiliary system of forward-backward stochastic delayed differential equations (FBSDDEs) with mutually orthogonal strategies. Under the assumption of a unique Nash equilibrium, we derive explicit solutions to the auxiliary FBSDDEs and hence obtain an explicit form of the open-loop Nash equilibrium based on a generalized Riccati equation developed in this work. Numerical examples are provided to validate the theoretical results.</p>