How to remove blur on the edge of the shape in After Effects..

That's the anti alaising. The position of the rectangle and / or the size of the rectangle is not full integers.

For example, a size of 53.2 and / or a position of 963.75 will cause this.

Just mark the layer and press p to see the positon proberty. Check the numbers. Next, click your way through to rectangle path and check the size. If this is not solving it, note that there is additional transformation set on the shape. So check the values there, too.

Get in touch with all the properties. You'll work with them all the time.

*Martin

This is where a full UI screenshot with the modified properties of the layer revealed would really help. You'll have to use the toolbar at the top of the reply field to add an image. Just press the U key twice to reveal everything going on with the layer, take a screenshot and send it in.

Edit: I see the .PNG now. You're looking at the layer at 1600% and the edges do not line up with the pixel grid. This could be anything from the layer position, anchor point or scale, or the Transform Rectangle 1> position or any other transform property, or the rectangle size. The only real way to judge the edges is at 100% Magnification (200% on an HR monitor) and Full resolution. 

The most common cause of this kind of a problem is comp resolution set to something other than auto or full, magnification factor set to something more than 100%, or the Comp panel Fast Previews set to draft.  There is no option to turn Continuous Rasterization off on a shape or a text layer.