With the rising energy price and the ever-increasing consciousness of environmental friendliness, it is becoming practically helpful for manufacturers to have a clear view on how the energy is consumed at their shop floors, what the corresponding energy cost is, and how to reduce the energy consumption or the energy cost. However, there is currently limited literature investigating the energy cost minimization in manufacturing through production scheduling under volatile energy prices. This paper proposes a generic mixed-integer linear programming model to enable the job scheduling on a single machine for the purpose of minimizing the necessary energy cost without exceeding the due date. The results given by a case study on a surface grinding machine demonstrate this scheduling methodology effectively contributes to the reduction of greenhouse gas emissions during peak time periods by shifting the production load to off-peak periods, and leads to energy-efficient, demand-responsive, and cost-effective manufacturing processes.