  We study Freidlin-Wentzell's large deviation principle for one dimensional
nonlinear stochastic heat equation driven by a Gaussian noise: $$\frac{\partial
u^\varepsilon(t,x)}{\partial t} = \frac{\partial^2 u^\varepsilon(t,x)}{\partial
x^2}+\sqrt{\varepsilon} \sigma(t, x, u^\varepsilon(t,x))\dot{W}(t,x),\quad t>
0,\, x\in\mathbb{R},$$ where $\dot W$ is white in time and fractional in space
with Hurst parameter $H\in(\frac 14,\frac 12)$. Recently, Hu and Wang ({\it
Ann. Inst. Henri Poincar\'e Probab. Stat.} {\bf 58} (2022) 379-423) studied the
well-posedness of this equation without the technical condition of
$\sigma(0)=0$ which was previously assumed in Hu et al. ({\it Ann. Probab}.
{\bf 45} (2017) 4561-4616). We adopt a new sufficient condition proposed by
Matoussi et al. ({\it Appl. Math. Optim.} \textbf{83} (2021) 849-879) for the
weak convergence criterion of the large deviation principle.
