Beam dynamics and rf designs of a 104 MHz ladder type IH-RFQ (L-IH-RFQ) accelerator are finished at Peking University for the acceleration of 14C+ from 40keV to 500keV. As a specific feature, the output beam energy spread is as low as 0.6% achieved with the internal discrete bunching method, which makes potential applications of RFQ feasible, such as accelerator mass spectrometry and ion implantation. Tolerances of the beam dynamics design are studied by means of changing the input beam parameters, and the results are quite satisfying. On the other hand, the L-IH-RFQ structure is employed, taking advantage of its mechanical stability and the absence of inter-electrode voltage asymmetry. Radio-frequency properties are studied and optimized for reducing power loss with Microwave Studio (MWS). Tuning of the field flatness and frequency is investigated in principle.