Here’s “CWM Method” of rooting your Samsung Galaxy S4.
Currently, this root method is only for the GT-i9500, GT-i9505, AT&T SGH-i337, Sprint SPH-L720, and Korean (E300S, E300K, E300L) until we have a stable, working CWM recovery for other models.
This root method works on Android 4.4.2 KitKat, 4.3 Jelly Bean and Android 4.4.2 KitKat for all models except AT&T SGH-i337. For SGH-i337, this root method works on 4.3 Jelly Bean and Android 4.4.2 KitKat.
For GT-i9505, AT&T SGH-i337, T-Mobile, Sprint SPH-L720, and Verizon, you can also use the other root method here.
For rooting Sprint S4 on MF9 firmware, see here.
Step 1. Power off you Galaxy S4 and hold down VolumeDown, Center Home, and Power buttons together for about 5 seconds.
Step 2. When you see the warning screen, let go of all buttons then hit the Volume Up button to enter ODIN Download mode.
Step 3. Connect a micro-USB cable from your Galaxy S4 to your computer.
Step 4. Next, download CWM recovery for your Galaxy S4. (Currently only GT-i9500, AT&T, and Sprint is available but I will be updating the page as soon as stable ones are available for other models.)