Hello there Jia Lee,
It sounds like we need to start troubleshooting wifi issues with the iPhone. Here is a great resource for that named iOS: Troubleshooting Wi-Fi networks and connections found here http://support.apple.com/kb/ts1398.
- Be sure that you are in range of your Wi-Fi router (access point).
- Tap Settings > Wi-Fi and turn Wi-Fi off and then on again.
- If unable to do so, see this article.
- Confirm that your Wi-Fi router and Cable or DSL modem are connected to power, turned on, and indicate that they are connected to the Internet.
- If not, refer to your network administrator or ISP for assistance.
- Restart your iOS device.
- Tap Settings > Wi-Fi and locate the Wi-Fi network to which you are connected. Then tap > and Forget this Network. Try to connect to your desired Wi-Fi network again.
- Note: You will need to enter your Wi-Fi password again if your desired network requires one.
- Turn your Wi-Fi router off and then on again2. If your ISP also provides cable or phone service, check with them before attempting this step to avoid interruption of service.
- Update your device to the latest version of software.
- Update your Wi-Fi router to the latest firmware2.
- For AirPort Base Stations, see this article for information about firmware updates.
And this section toward the bottom as well.
- If you are using a public or commercial network that requires a login or subscription, see this article for more information.
- Check to see if you have a self-assigned IP address:
- Tap Settings > Wi-Fi and locate the Wi-Fi network to which you are connected. Then tap >.
- If your IP address is 169.254.xxx.xxx, see this article.
- If you do not have a self-assigned IP address, see if other Wi-Fi devices on your network have Internet access.
- If they do not, consult with your network administrator or ISP for further assistance.
- If they do, reset network settings on your device by tapping Settings > General > Reset > Reset Network Settings.
- Note: This will reset all network settings including: previously connected Wi-Fi networks and passwords, recently used Bluetooth accessories, VPN and APN settings.
It is also worth noting that a great test would be to connect to a different wifi network, and try to download an app there. That way if it works there, then we know its something to do with the router being used. If the issue persists on a different network then we know the issue is more than likely with the phone.