This paper presents a detailed study of the two-dimensional (2D) differential geometric (DG) guidance problem, as well as its iterative solution and initial conditions. The DG guidance curvature command is transformed from an arc length system to the time domain using the classical DG theory. Subsequently, an algorithm for commanded angle-of-attack is developed to formulate the DG guidance system, whose iterative solution is established based on Newton’s iterative algorithm. Moreover, a flight control system is presented using the classical PID controller so as to form the DG guidance and control system. Finally, a new necessary initial condition is deduced to guarantee the capture of a high-speed target. Simulation results demonstrate that Newton’s iterative algorithm works well and accurately in DG guidance problems and the proposed DG guidance law exhibits similar performance to the proportional navigation guidance (PNG) law in the case of intercepting a non-maneuvering target. However, the proposed method performs better than PNG in the case of intercepting a maneuvering target.