In the present work, the relativistic quantum motion of massless fermions in a helicoidal graphene nanoribbon under the influence of a uniform magnetic field is investigated. Considering a uniform magnetic field (B) aligned along the axis of helicoid, this problem is explored in the context of Diracequation in a curved space-time. As this system does not support exact solutions due to considered background, the bound-state solutions and localdensity of states (LDOS) are obtained numerically by means of the Numerovmethod. The combined effects of width of the nanoribbon (D), length ofribbon (L), twist parameter (w), andBon the equations of motion and LDOSare analyzed and discussed. It is verified that the presence ofBproduces aconstant minimum value of local density of state on the axis of helicoid,which is possible only for values large enough ofw,in contrast to the case for B=0 already s...