This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society©: 2014 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved ; We present a new methodology to generate mock halo or galaxy catalogues, which have accurate clustering properties, nearly indistinguishable from full N-body solutions, in terms of the one-point, two-point, and three-point statistics. In particular, the agreement is remarkable, within 1% up to k = 0:65 hMpc-1 and down to r = 10 h-1 Mpc, for the power spectrum and two-point correlation function respectively, while the bispectrum agrees in general within 20% for different scales and shapes. Our approach is based on the Zel’dovich approximation, however, effectively including with the simple prescriptions the missing physical ingredients, and stochastic scale-dependent, non-local and nonlinear biasing contributions. The computing time and memory required to produce one mock is similar to that using the log-normal model. With high accuracy and efficiency, the effective Zel’dovich approximation mocks (EZmocks) provide a reliable and practical method to produce massive mock galaxy catalogues for the analysis of large-scale structure measurements