  By extending the usual two-mode squeezing operator $S_{2}=\exp [ i\lambda
(Q_{1}P_{2}+Q_{2}P_{1}) ] $ to the three-mode squeezing operator $S_{3}=\exp
{i\lambda [ Q_{1}(P_{2}+P_{3}) +Q_{2}(P_{1}+P_{3}) +Q_{3}(P_{1}+P_{2}) ]} $, we
obtain the corresponding three-mode squeezed coherent state. The state's
higher-order properties, such as higher-order squeezing and higher-order
sub-Possonian photon statistics, are investigated. It is found that the new
squeezed state not only can be squeezed to all even orders but also exhibits
squeezing enhancement comparing with the usual cases. In addition, we examine
the violation of Bell-inequality for the three-mode squeezed states by using
the formalism of Wigner representation.
