This paper is devoted to the pricing of variance and volatility swaps in energy market. We found explicit variance swap formula and closed form volatility swap formula (using Brockhaus-Long approximation) for energy asset with stochastic volatility that follows continuous-time GARCH (1,1) model (mean-reverting) (or Pilipovi\'{c} one-factor model). Numerical example is presented for AECO Natural Gas Index (1 May 1998-30 April 1999).