This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has at least two main advantages: (a.) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS, rather than constrained NLP algorithms, therefore the computational efficiency is increased; (b.) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, so the minimal number of time intervals that under desired integration tolerance can be estimated, for refining the control and state profiles. After elaborating the principles of the approach, a numerical algorithm is put forward in detail. Two classic cases are adopted to test the algorithm and the fine results shows the effectiveness and efficiency of the algorithm. This paper considers problems without path constraints, dealing with path constraints requires extra techniques, and will be studied in the second paper.