We first design and optimize a hollow-core conjoined-tube antiresonant fiber (CT-ARF) for weakly coupled $\mathrm{LP_{01}}$ and $\mathrm{LP_{11}}$ modes transmission. The critical core radii for the weak-coupling condition in the CT-ARFs with 4 to 8 tubes are obtained. Using numerical simulation, we demonstrate that by tuning the glass sheets positions in cladding tubes the confinement losses (CLs) of higher-order modes (HOMs) $\mathrm{LP_{21}}$ , $\mathrm{LP_{02}}$ , and $\mathrm{LP_{31}}$ can be maximized through core-cladding mode coupling. Among the CT-ARFs with 4 to 8 tubes, the 6-tube one is proved to have the lowest CLs and bending losses of $\mathrm{LP}_{01}$ and $\mathrm{LP}_{11}$ modes and the highest CL ratios between the undesired HOMs and the two guided modes. In the designed 6-tube CT-ARF, $\mathrm{LP_{01}}$ and $\mathrm{LP_{11}}$ modes have low CLs in the transmission band of 1.31–1.65 $\mu \text{m}$ . The minimum CLs of $\mathrm{LP_{01}}$ and $\mathrm{LP_{11}}$ modes are $\text{1.7}\times \text{10}^{-4} \text{ dB/m}$ and $\text{3.1} \times \text{10}^{-3} \text{ dB/m}$ in the C-band (1.53–1.565 $\mu \text{m}$ ) respectively. A 10 cm bend has a weak influence on the two guided modes. The CL ratio between the lowest loss HOM and $\mathrm{LP}_{11}$ mode keeps $>\!\!150$ in the wavelength range from 1.25–1.65 $\mu \text{m}$ , which ensures the high purity of $\mathrm{LP_{01}}$ and $\mathrm{LP}_{11}$ modes. The fabrication tolerances of the fiber are discussed.