The paper considers the class of non-cooperative non-autonomous linear-quadratic differential games with continuous updating of information. Continuous updating of information involves changing the parameters of the differential game continuously at each moment in time. This approach allows you to simulate real processes in which players do not know the whole future, but can predict the dynamics and payoff functions on some small information horizon. Sufficient conditions for the existence of a Nash equilibrium of a non-autonomous linear-quadratic differential game with continuous updating of information are obtained.