Pb-208 is a doubly magic nucleus which has been studied extensively by many experiments and nuclear models. Its properties, such as excitation energies, spins, and parities of the ground and excited states are well known. However, some gamma transitions with E-gamma > 3 MeV from the excited states to the ground state in Pb-208 have never been observed. The intensities of these gamma transitions are important issues for 0 nu beta beta decay searches because these transitions can make non-negligible background signals depending on their intensities. We conducted a measurement to search for the 3197.7, 3475.1, and 3708.4 keV transitions, which are emitted from the second, third, and fourth excited states in Pb-208, respectively. A 2 kg ThO2 sample was measured using a 100% relative efficiency high-purity germanium detector for 39.5 days at Y2L, an underground laboratory in Yangyang, Korea. We improved upper limits for intensities of the 3197.7, 3475.1, and 3708.4 keV gamma transitions as <1.2 x 10(-4)%, <1.4 x 10(-4)%, and <1.2 x 10(-4)%, respectively. These upper limits are at least a factor of 19 better than the previous results.