Blender 2.79c finally supports the vertex paint alpha channel!

It hasn’t released yet, but it is in the nightly builds here:

(choose the one tagged ‘Official’, not 2.8)

Hi! Sorry but I can’t find where is it feature. Vertex Paint mode still have only 3 colors in color picker.

First of all, it’s important to get the latest 2.79 version, as stated. It isn’t implemented properly anywhere else yet. Secondly, the implementation isn’t ideal and the devs know that. That said, you need to use the substract brush in vertex paint mode. From what I gathered, the alpha on the brush is always set to 1. So, substracting changes the alpha channel towards 0, adding adds it back (duh).
Best practice I found is to finish any actual coloring and only then focus on alpha. When you’re substracting or adding, don’t forget to set your brush color to black. Black has 0 0 0 on the RGB channels, so you only will change the alpha channel this way (0, 0, 0, 1). If you have white or any color, you’ll end up changing the vertex colors. Use the strength of the brush to scale the alpha strength when drawing.