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In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. An artificial stabilizing term Aτ2∂Δ2u∂t A τ 2 ∂ Δ 2 u ∂ t $ A{\tau }^2\frac{\mathrm{\partial }{\Delta }^2u}{\mathrm{\partial }t}$ is added to the physical model to achieve energy stability, with ETD-based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed 𝓁∞(0,T;𝓁2) l ∞ (0 , T ; l 2) $ {\mathcal{l}}^{\mathrm{\infty }}(0,T;{\mathcal{l}}^2)$ error analysis are provided based on the energy method, with a careful estimate of the aliasing error. In addition, numerical experiments are presented to demonstrate the energy decay and convergence rate. [ABSTRACT FROM AUTHOR]