Eating speed is an important indicator that has been widely investigated in nutritional studies. The relationship between eating speed and several intake-related problems such as obesity, diabetes, and oral health has received increased attention from researchers. However, existing studies mainly use self-reported questionnaires to obtain participants' eating speed, where they choose options from slow, medium, and fast. Such a non-quantitative method is highly subjective and coarse at the individual level. This study integrates two classical tasks in automated food intake monitoring domain: bite detection and eating episode detection, to advance eating speed measurement in near-free-living environments automatically and objectively. Specifically, a temporal convolutional network combined with a multi-head attention module (TCN-MHA) is developed to detect bites (including eating and drinking gestures) from IMU data. The predicted bite sequences are then clustered into eating episodes. Eating speed is calculated by using the time taken to finish the eating episode to divide the number of bites. To validate the proposed approach on eating speed measurement, a 7-fold cross validation is applied to the self-collected fine-annotated full-day-I (FD-I) dataset, and a holdout experiment is conducted on the full-day-II (FD-II) dataset. The two datasets are collected from 61 participants with a total duration of 513 h, which are publicly available. Experimental results show that the proposed approach achieves a mean absolute percentage error (MAPE) of 0.110 and 0.146 in the FD-I and FD-II datasets, respectively, showcasing the feasibility of automated eating speed measurement in near-free-living environments.