Open a file with the Size 468 x 60 pixels. set you foreground to #d00059 and background to #89001d and create a linear gradient.

Now write whatever you want in my case i wrote LayoutPrince.com.

Select a Rounded rectangle tool and draw the shape in any color and apply layer styles as follows.

Now write your text. Here I am using three text layers. After writing the text get the duplicate of each text layer and rasterized them.

Select the first rasterized layer _____ go to filter _____ Blur _____ Motion blur and apply as follows.

Now we will go for Animation. Open Animation window. We have 6 text layers so we will create 6 Frames by clicking on "Duplicates selected frames" icon.

Frame 1:

First Text Layer will be visible
Delay 2.0 sec.

Frame 2:

Duplicate of First  Text Layer will be visible
Delay 0.1 sec.

Frame 3:

Second Text Layer will be visible
Delay 2.0 sec.

Frame 4:

Duplicate of Second  Text Layer will be visible
Delay 0.1 sec.

Frame 5:

Third Text Layer will be visible
Delay 2.0 sec.

Frame 6:

Duplicate of third Text Layer will be visible
Delay 0.1 sec.