A sinuous antenna is a frequency-independent antenna known for its wide bandwidth and consistent gain, which makes it valuable in broadband applications such as ultrawideband (UWB) radar and ground-penetrating radar (GPR). However, sinuous antennas tend to be rather large. Consequently, numerous studies have explored miniaturization methods, with the gap-loading method emerging as a prominent approach. Unfortunately, it is still difficult to achieve broad bandwidths for conventional miniaturized sinuous antennas. In this paper, we use a novel approach incorporating a meander shape into the sinuous curve and employing gap loading with meandering. This innovative technique results in the development of a fractal-structured two-arm sinuous antenna characterized by an ultra-compact size and significantly expanded bandwidth. Adding a meander line in the outermost part maximizes the capacitance, thereby enhancing the gap-loading effect and minimizing the overall size of the sinuous antenna. In addition, the introduction of an inner meander line increases the inductance, contributing to a further expansion of the antenna’s bandwidth. For example, the electrical length of the antenna without the meander line is 0.552 × 0.552 × 0.052 λg3, while the electrical length of the antenna with the meander line is only 0.445 × 0.445 × 0.036 λg3, i.e., 19.4% smaller. The antenna lacking the outermost meander line exhibits a 10 dB impedance bandwidth, spanning from 0.74 to 10.53 GHz. In contrast, the antenna featuring the outermost meander line has a 10 dB impedance bandwidth, extending from 0.51 to 10.72 GHz, which results in a remarkable enhancement in the fractional bandwidth (by 8.1%). Hence, the proposed antenna design is a good candidate for broadband applications that require miniaturization.