We investigated the growth mechanisms of wormlike micelles formed by star-type trimeric surfactant (3C(12)trisQ) with a hydrocarbon chain length of 12 in an aqueous solution. A 3C(n)trisQ molecule consists of three hydrocarbon chains and three hydrophilic groups connected by spacer chains, where n is the carbon number in the hydrocarbon chain. Our recent studies showed that the aggregates formed by 3C(12)trisQ exhibited sphere-to-rod transition and the growth of wormlike micelles in an aqueous solution in the absence of salt. We performed small-angle neutron scattering (SANS) and rheological measurements and investigated the aggregation behavior of 3C(12)trisQ with various surfactant volume fractions. All SANS profiles for the 3C(12)trisQ indicated peak-profiles in the q range of 0.02 angstrom(-1) < q <0.05 angstrom(-1), where the magnitude of the scattering vector q is defined by q = 4 pi sin(theta/2)/lambda (lambda and theta represent the wavelength and scattering angle, respectively). These peaks were attributed to repulsive interparticle interactions between the micelles. The volume fraction dependence of the SANS peak-position was in agreement with the rheological behavior. These results suggest that 3C(12)trisQ shows sphere-to-rod transition and can produce wormlike micelles in the absence of salt. To determine the structural parameters quantitatively, model-fitting analysis was performed using a charged cylindrical or charged ellipsoidal particle scattering function. The radius, length, and number of water molecules per surfactant molecule (n(w)) inside the micelles were evaluated. The length increased and the n(w), value decreased with increasing phi, indicating that the growth of a wormlike micelle accompanies the extrusion of water from the micelle. The end-cap energies of star-type trimeric, gemini, and monomeric surfactants were evaluated from phi dependence of zero-shear viscosity. We found that wormlike micelles formed by 3C(12)trisQ exhibited a higher end-cap energy than gemini surfactant.