No unless you drop to 0 HP in Beast Form
Page 67 of the PHB states
"When you revert to your normal form, you return to the number of hit
points you had before you had transformed".
Example: Let's say your normal form has 15 HP and then you transform into a 10 HP beast form. Later you take 9 damage which drops you to 1 HP(while in beast form) and then you revert back to normal. In that case your HP will be 15 HP not 1 HP cause you assume the HP of your normal form before you had transformed.
The Exception: 0 HP
The exception to this rule being when you drop to 0 HP, in which case all excess damage is applied to your normal form.
Example: If your beast form had 10 HP and you take 12 HP, you will return to your normal form and take 2 excess damage.