Strong electromagnetic fields produced in the non-central heavy-ion collisions can induce vector meson photoproduction.In this paper,we study the photoproduction J/ψ and φ mesons in the relativistic heavy-ion collision from ultra-peripheral nuclear collisions to peripheral hadronic heavy ion collisions.And then include both initial hadronic production and thermal production in quark-gluon plasma(QGP).We find,for the charm anti-charm bound state J/ψ,the photoproduced J/ψs are mainly in the very low momentum region and clearly exceed the hadronic production.However,considering the thermal production of strange quark anti-quark pairs in QGP produced in relativistic heavy-ion collisions,the photoproduced φ is usually smaller than the thermal production and only evident at very peripheral collisions as even their photoproduction is much larger than J/ψ.