In this work, we investigate the influence of quasi-periodic modulation on the localization properties of one-dimensional non-Hermitian cross-stitch lattices with flat bands. The crystalline Hamiltonian for this non-Hermitian cross-stitch lattice is given by:

\hatH=\displaystyle\sum\limits_n\leftt(a_n^\dagger b_n + b_n^\daggera_n ) + J\mathrme^h\left(a_n^\daggerb_n + 1 + a_n^\dagger a_n + 1 + Ab_n^\daggera_n + 1 + Ab_n^\daggerb_n + 1\right) + J\mathrme^ - h \left(Aa_n + 1^\daggerb_n + a_n + 1^\daggera_n + b_n + 1^\daggera_n + Ab_n + 1^\daggerb_n\right)\right with A =\pm 1. When A = 1, the clean lattice supports two bands with dispersion relations E_0=- t, E_1=4\cos (k - \mathrmih) + t. The compact localized states (CLSs) within the flat band E₀ are localized in one unit cell, indicating that the system is characterized by the U = 1 class. Conversely, for A = –1, there are two flat bands in the system: E_\pm=\pm\sqrtt^2 + 4. The CLSs within the flat bands are localized in two unit cells, indicating that the system is marked by the U = 2 class. After introducing quasi-periodic modulations \varepsilon_n^\beta=\lambda_\beta\cos(2\pi\alpha n + \phi_\beta) (\beta=\a,b\), delocalization-localization transitions can be observed by numerically calculating the fractal dimension D₂ and imaginary part of the energy spectrum \ln|\rmIm(E)|. Our findings indicate that the symmetry of quasi-periodic modulations plays an important role in determining the localization properties of the system. For the case of U=1, the symmetric quasi-periodic modulation leads to two independent spectra \sigma_f and \sigma_p. The \sigma_f retains its compact properties, while the \sigma_p owns an extended-localized transition at \lambda_\mathrmc1=4M with M=\max\\mathrme^h,\;\mathrme^ - h\. However, in the case of antisymmetric modulation, the system exhibits an exact mobility edge \lambda_\mathrmc2=2\sqrt2|E - t|M. For the U = 2 class, all the eigenstates remain localized under any symmetric quasi-periodic modulation. In the case of antisymmetric modulation, all states transition from multifractal to localized states as the modulation strength increases, with a critical point at \lambda_\mathrmc3=4M. This work expands the understanding of localization properties in non-Hermitian flat-band systems and provides a new perspective on delocalization-localization transitions.