In the paper the solvability of a boundary value problem with a non-local boundary condition for a pseudo-hyperbolic equation is investigated. The studied equation is sometimes called the Kirchhoff equation, Klein-Gordon equation and in general case, the Sobolev equation. The boundary condition in this paper is distinguished by nonlocality and nonlinearity. The existence and uniqueness of a weak generalized solution of the problem is proved. A time locality theorem is proved for the existence and uniqueness of a weak generalized solution. The Galerkin method, a priori estimates of approximate solutions, the necessary interpolation inequalities, the inequalities of Young, Gelder and Minkowski, the lemmas of Gronwall and Bihari were used to prove the existence and uniqueness of the problem's solution. The need to consider and study initial boundary value problems for a nonlinear pseudo-hyperbolic equation follows from practical needs. In this paper, it is shown that all derivatives of the solution in time involved in the equation belong to the space L