Recommender systems are an important kind of learning systems, which can be achieved by latent-factor (LF)-based collaborative filtering (CF) with high efficiency and scalability. LF-based CF models rely on an optimization process with respect to some desired latent features; however, most of them employ first-order optimization algorithms, e.g., gradient decent schemes, to conduct their optimization task, thereby failing in discovering patterns reflected by higher order information. This work proposes to build a new LF-based CF model via second-order optimization to achieve higher accuracy. We first investigate a Hessian-free optimization framework, and employ its principle to avoid direct usage of the Hessian matrix by computing its product with an arbitrary vector. We then propose the Hessian-free optimization-based LF model, which is able to extract latent factors from the given incomplete matrices via a second-order optimization process. Compared with LF models based on first-order optimization algorithms, experimental results on two industrial datasets show that the proposed one can offer higher prediction accuracy with reasonable computational efficiency. Hence, it is a promising model for implementing high-performance recommenders.