Existing automated essay scoring (AES) models rely on rated essays for the target prompt as training data. Despite their successes in prompt-dependent AES, how to effectively predict essay ratings under a prompt-independent setting remains a challenge, where the rated essays for the target prompt are not available. To close this gap, a two-stage deep neural network (TDNN) is proposed. In particular, in the first stage, using the rated essays for non-target prompts as the training data, a shallow model is learned to select essays with an extreme quality for the target prompt, serving as pseudo training data; in the second stage, an end-to-end hybrid deep model is proposed to learn a prompt-dependent rating model consuming the pseudo training data from the first step. Evaluation of the proposed TDNN on the standard ASAP dataset demonstrates a promising improvement for the prompt-independent AES task.