A two-dimensional immiscible water meniscus deformation phenomena on a moving tip in a channel has been investigated by using lattice Boltzmann method involving two-phase model. We studied the behavior of a water meniscus between the tip and a solid surface. The contact angles of the tip and a solid surface considered are in the range from $10^{circ}$ to $170^{circ}$. The velocity of the tip used in the study are 0.01, 0.001, and 0.0001. The shapes of tip considered are rectangular and circular. The behavior of water confined between the tip and a solid surface depends on the contact angles of the tip and a solid surface, and the tip velocity. When the tip is moving, we can observe the various behaviors of shear deformation of a water meniscus. As time goes on, the behavior of a water meniscus can be classified into three different patterns which are separated from the tip or adhered to the tip or sticked to a solid surface according to the contact angles and the tip velocity.