The regularity criteria of the three-dimensional incompressible Boussinesq equations are mainly considered. It is proven that if one component of the velocity field satisfies  ∫

T*

0

‖u

i

‖

p

Ｈ

(1/2+2/p

(R3)

ds

<

∞

p∈(2

∞)

i=1

2

3 to the Boussinesq equations

the local solution can be continuously extended to the endpoint. This result improves and develops some known regularity criteria of the threedimensional incompressible Boussinesq equations

which is a supplement to the regularity theory.