Quantum gates are essential for realizing quantum computing. How to achieve high-fidelity quantum gate operations, in the meanwhile maintaining high robustness against multiple control errors has been an important issue. Among various methods to realize quantum gates, using the geometric phase to construct the gates is an effective way, as the geometric phase has built-in noise-resilient characteristics. A general theoretical scheme to realize non-adiabatic non-abelian geometric quantum gates is to force the system to evolve along one of the time-dependent basis, then obtain the constrained conditions for the pulses. However, there might be some singular points in the constructed Rabi frequency, which are not preferred in certain quantum systems such as superconducting quantum circuits. In this work, we proposed a general condition to eliminate such singular points and developed smooth pulses in the three-level system with a Λ configuration. For the purpose of optimizing the gate performance, we introduced a new parameter k, which serves as an additional degree of freedom and is then used to modulate the shape of the pulses. The influence of parameter k on the gate performance has been numerically investigated in various aspects utilizing the Lindblad master equation, where the decoherence effects are considered. We taking superconducting qubit gates as an example, studied the robustness of pulses produced by different k values by introducing the detuning error and the Rabi frequency error. We found that the pulses with larger k values are more robust againstthe detuning error, while the Rabi error rate is not sensitive to k. The reason is that a larger k generates a higher instantaneous amplitude in the Rabi frequency when the gate duration is fixed, so that the perturbative effect is relatively smaller. On the other hand, the Rabi error is proportional to the Rabi frequency by definition, so its robustness is irrelevant to the pulse envelope. These results show that the theoretical scheme in this work provides us with a simple and feasible way for constructing the pulses for implementing the non-adiabatic geometric quantum gates.