Motivated by importance of the cosmological constant on structure of the hybrid neutron star. In other words, we want to investigate the structure of neutron stars by considering both the effects of the cosmological constant and the existence of quark matter for neutron stars in Einstein gravity. For this purpose, we use of a suitable equation of state (EoS) which includes a layer of hadronic matter, a mixed phase of quarks and hadrons, and, a quark matter in core. In order to investigate the effect of the cosmological constant on the structure of hybrid neutron stars, we utilize of modified TOV equation in Einstein-Λ gravity. Then we plot the mass-radius diagram for different value of the cosmological constant. Our results show that for small values of the cosmological constant (Λ), especially for the cosmological constant from the cosmological perspective (Λ = 10 −52 m −2 ), Λ has no significant effect on structure of hybrid neutron star. But for bigger values, for example, by considering Λ > 10 −14 m −2 , this quantity affects on the maximum mass and radius of these stars. The maximum mass and radius of these stars decrease by increasing the cosmological constant Λ. Also by determining and analyzing radius, compactness, Kretschmann scalar and gravitational redshift of a hybrid neutron star with M = 1.4M ⊙ in the presence of the cosmological constant, we find that, by increasing Λ, this star is contracted. Also, our results about dynamical stability show that these stars satisfy this stability.