In this paper, we propose the design of economic model predictive control (MPC) systems based on a single-step approach of the adaptive MPC technique proposed for a class of uncertain nonlinear systems subject to parametric uncertainties and exogenous variables. The framework considered assumes that the economic function is a known function of constrained system's states, parameterised by unknown parameters. The objective and constraint functions may explicitly depend on time, which means that our proposed method is applicable to both dynamic and steady state economic optimisation. A simulation example is used to demonstrate the effectiveness of the design technique.