In this work, we consider secure multiparty computation (MPC) in the asynchronous network setting. MPC allows n parties to compute a public function on their private inputs against an adversary corrupting at most t of them. We consider both communication complexity and round complexity of asynchronous MPC (AMPC) with the optimal resilience \(n=3t+1\) . Without fully homomorphic encryptions, the best-known result in this setting is achieved by Coretti, Garay, Hirt, and Zikas (ASIACRYPT 2016), which requires \(O(|C|n^3\kappa )\) bits of communication assuming one-way functions, where \(\kappa \) is the security parameter. On the other hand, the best-known non-constant-round AMPC by Goyal, Liu, and Song (CRYPTO 2024) can achieve O(|C|n) communication in the information-theoretic setting. In this work, we give the first construction of a constant-round AMPC with \(O(|C|n\kappa )\) bits of communication that achieves malicious security with abort assuming random oracles. We provide new techniques for adapting the MPC-in-the-head framework in the asynchronous network to compute a constant-size garbled circuit.