var client = new TcpClient();
var result = client.BeginConnect("remotehost", this.Port, null, null);

var success = result.AsyncWaitHandle.WaitOne(TimeSpan.FromSeconds(1));

if (!success)
{
    throw new Exception("Failed to connect.");
}

// we have connected
client.EndConnect(result);

.Net 4.5的簡便寫法

var client = new TcpClient();
if (!client.ConnectAsync("remotehost", remotePort).Wait(1000))
{
    // connection failure
}

代碼出處： https://stackoverflow.com/questions/17118632/how-to-set-the-timeout-for-a-tcpclient

C# 給TcpClient的Connect方法設置超時時間