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We report measurements of the branching fractions singly Cabibbo-suppressed decays $\Lambda_c^+ \to p \eta$ and \pi^0$ using full Belle data sample corresponding to an integrated luminosity 980.6 $\rm fb^{-1}$. The were collected by detector at KEKB $e^{+}$$e^{-}$ asymmetric-energy collider. A clear $\Lambda_c^+$ signal is seen in invariant mass distribution $p \eta$. yield process $7734 \pm 263$; from this, we measure ratio ${\cal B}(\Lambda_c^+ \eta)/{\cal K^- \pi^+) = (2.258 0. 077(\rm stat. ) 0.136(\rm syst. ))\times 10^{-2}$, which infer fraction \eta) (1.42 0.05(\rm stat.) 0.11(\rm syst.)) \times 10^{-3}$. In addition, no significant for found so upper limit on \pi^0)<8.0 10^{-5}$ 90\% credibility level set, more than three times better best current limit.