A linear lighting device with light-emitting diodes comprising at least: - an extended body which comprises at least one surface receiving at least one substrate supporting one linear light source comprising at least one row of light-emitting diodes aligned along a longitudinal axis of the body and at least partially defining at least one extended linear lighting chamber wherein the diodes are located, - an extended linear cover which closes the lighting chamber, characterized in that the cover forms, in relation with the linear source, an at least translucent linear lens, having a longitudinal axis parallel to the longitudinal axis of the body, with an outer face emitting light and an inner face receiving light from the diodes, among which - the emitting face, as seen in straight cross-section, has a central and protruding portion having a generally convex shape edged with two plane side portions, with each edge of the central portion forming, with the corresponding plane portion, an angle, as measured outside the linear lens, smaller than or equal to 95°, and - the receiving face, as seen in straight cross-section, comprises: ∘ an at least partially concave central region located opposite the central region of the emitting face to form a cavity accommodating the diodes, ∘ two plane side portions substantially parallel to the plane side portions of the emitting face to form two side wings diffusing light which edge the linear lens, with each edge of the central region forming, with the corresponding plane portion, an angle, as measured inside the linear lens, greater than or equal to 100° and preferably greater than 110°. - an extended body which comprises at least one surface receiving at least one substrate supporting one linear light source comprising at least one row of light-emitting diodes aligned along a longitudinal axis of the body and at least partially defining at least one extended linear lighting chamber wherein the diodes are located, - an extended linear cover which closes the lighting chamber, characterized in that the cover forms, in relation with the linear source, an at least translucent linear lens, having a longitudinal axis parallel to the longitudinal axis of the body, with an outer face emitting light and an inner face receiving light from the diodes, among which - the emitting face, as seen in straight cross-section, has a central and protruding portion having a generally convex shape edged with two plane side portions, with each edge of the central portion forming, with the corresponding plane portion, an angle, as measured outside the linear lens, smaller than or equal to 95°, and - the receiving face, as seen in straight cross-section, comprises: ∘ an at least partially concave central region located opposite the central region of the emitting face to form a cavity accommodating the diodes, ∘ two plane side portions substantially parallel to the plane side portions of the emitting face to form two side wings diffusing light which edge the linear lens, with each edge of the central region forming, with the corresponding plane portion, an angle, as measured inside the linear lens, greater than or equal to 100° and preferably greater than 110°. ∘ an at least partially concave central region located opposite the central region of the emitting face to form a cavity accommodating the diodes, ∘ two plane side portions substantially parallel to the plane side portions of the emitting face to form two side wings diffusing light which edge the linear lens, with each edge of the central region forming, with the corresponding plane portion, an angle, as measured inside the linear lens, greater than or equal to 100° and preferably greater than 110°.