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The precise measurement of the light neutral meson production ($\pi^0$, $\eta$) in high energy pp collisions at the LHC can be used as a constraint for fragmentation functions and parton density functions needed by pQCD calculations. Additionally, those measurements provide an essential input for direct photon analyses. In pp collisions, the dependence of the neutral meson cross section on the event particle multiplicity provides a baseline to study the presence of effects that could be interpreted as the creation of the quark-gluon plasma in the collision, as other measurements in small collision systems might indicate. In ALICE, neutral mesons can be reconstructed via several partially independent reconstruction techniques where the decay photons were detected with the electromagnetic calorimeter (EMCal), the photon spectrometer (PHOS), or via the central tracking system using $e^+e^-$ pairs from conversions in the detector material. The combination of these methods allows for a large $p_{\rm T}$ coverage as well as small statistical and systematic uncertainties. In this talk the invariant cross sections of the $\pi^0$ and $\eta$ production as a function of $p_{\rm T}$ in pp collisions at $\sqrt{s}$ = 13 TeV with ALICE, focusing on the dependence on the event multiplicity, will be presented.
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