Large-scale speech self-supervised learning (SSL) has emerged to the main field of speech processing, however, the problem of computational cost arising from its vast size makes a high entry barrier to academia. In addition, existing distillation techniques of speech SSL models compress the model by reducing layers, which induces performance degradation in linguistic pattern recognition tasks such as phoneme recognition (PR). In this paper, we propose FitHuBERT, which makes thinner in dimension throughout almost all model components and deeper in layer compared to prior speech SSL distillation works. Moreover, we employ a time-reduction layer to speed up inference time and propose a method of hint-based distillation for less performance degradation. Our method reduces the model to 23.8% in size and 35.9% in inference time compared to HuBERT. Also, we achieve 12.1% word error rate and 13.3% phoneme error rate on the SUPERB benchmark which is superior than prior work.