We introduce an equilibrium model on insider trading under asymmetric information in continuous time which incorporates adverse selection and inventory cost. In contrast to the classical Kyle-Back framework, we prescribe in our setting the evolution of the efficient price of the traded asset as an arithmetic Brownian motion which helps characterizing the criteria for equilibrium. In equilibrium, The insider's optimal trading strategy and the market maker's pricing rule under perfect competition are given by the solution to a system of ordinary differential equations and integral equations. Closed-form solution is obtained in the case where inventory cost is neglected. This solution recovers a version of time-dependent Kyle's lambda in our setting.