Previously, a linear relationship has been found between net energy intake (NEI) and dietary chewing index (CI) of the diet for different types of cattle. Therefore, we propose to generalize and calibrate this relationship into a new model for direct prediction of NEI by dairy cows from CI values (CINE; min/MJ of NE). Furthermore, we studied the forage-to-concentrate substitution rate in this new NEI model. To calibrate the model on a diverse set of situations, we built a database of mean intake from 14 production experiments with a total of 986 primi- and multiparous lactating dairy cows of different breeds fed 136 different diets ad libitum. The NEI were estimated by the Nordic feed evaluation system. The CINE value of diets was estimated from the intake of concentrate, intake of forage neutral detergent fiber (NDFf), particle length of forage, indigestible NDFf/NDFf, body weight, NDFf/body weight, and the content of NE in DM. We show that the slope values in this regression are proportional to the squared intercepts, giving the nonlinear equation NEI=NEI0-k×NEI0(a)×CINE, where the parameter k represents the decline in NEI with the increasing CINE of the diet and a was estimated to have a value of 2, implying a constant maximum daily chewing time. The intercept NEI0 in the regression of NEI on CINE may be interpreted as metabolic net energy intake capacity of the cows fed without physical constraints on intake. Based on experimental data, the maximum chewing time was estimated as 1/(4 × k). The NEI0 values were parameterized as a linear function of metabolic body size, energy-corrected milk yield (kg/d), days in milk, and days in milk squared. Prediction accuracy was evaluated by mean square prediction error (MSPE) and its decomposition into central tendency, regression, and disturbance, across and within experiments on independent data from 19 experiments including 812 primi- and multiparous lactating dairy cows of different breeds fed 80 different diets ad libitum. The NEI model predicted NEI with an MSPE of 8% of observed, and across the 19 experiments the error central tendency, error regression, and error disturbance were 4.2, 40.6, and 84.9% of MSPE, respectively. The described intake model implies a variable forage-to-concentrate substitution rate as a nonlinear function of NEI0, CINE of forage, and supplementation of concentrate.