Split-connection type proxies have been proposed to improve TCP (Transmission Control Protocol) throughput in network environment with wireless LANs. A proxy is placed at the boundary of a wireless LAN (WLAN) and a wired network and it splits a TCP connection into two virtual TCP connections. We proposed a split-connection type proxy called MDA-Proxy (Modified Decreasing-ACK Proxy), which increases throughput of upflows (flows from wireless hosts to wired hosts) by decreasing the number of ACKs in a WLAN. MDA-Proxy uses two parameters, ack-stock and delay-timer, for each connection. The former controls the number of ACKs sent to a WLAN and the latter is used to recover from losses and delays of ACKs in a wired network. However, it is assumed that MDA-Proxy uses fixed values of the two parameters and their automatic tuning in response to network situation remains to be future work. In this paper, we propose a new type of proxy called ASA-Proxy (Ack-Stock Autotunning Proxy), which automatically tunes the two parameters in MDA-Proxy. Ack-stock is tuned comparing throughputs before and after its changing so that throughput of the connection becomes large, and delay-timer is replaced by the normal TCP retransmission timer because it is better than a fixed value of delay-timer for the inference of losses and delays of ACKs in a wired network. Extensive simulation runs show that ASA-Proxy is superior to MDA-Proxy.