In open-set recognition (OSR), classifiers should be able to reject unknown-class samples while maintaining high closed-set classification accuracy. To effectively solve the OSR problem, previous studies attempted to limit latent feature space and reject data located outside the limited space via offline analyses, e.g., distance-based feature analyses, or complicated network architectures. To conduct OSR via a simple inference process (without offline analyses) in standard classifier architectures, we use distance-based classifiers instead of conventional Softmax classifiers. Afterwards, we design a background-class regularization strategy, which uses background-class data as surrogates of unknown-class ones during training phase. Specifically, we formulate a novel regularization loss suitable for distance-based classifiers, which reserves sufficiently large class-wise latent feature spaces for known classes and forces background-class samples to be located far away from the limited spaces. Through our extensive experiments, we show that the proposed method provides robust OSR results, while maintaining high closed-set classification accuracy.