An efficient aeronautical telecommunication network (ATN) is proposed in this paper based on adaptive multibeam antenna arrays and high-altitude platforms (HAPs). First, the network structure is demonstrated, and its geometry is analyzed based on a geocentric coordinate system that converts the global positioning system (GPS) and altitude data of aircrafts and HAPs into direction-of-arrival (DOA) information which is required for subsequent beamforming operation. The antenna array is then formed by designing a low-profile dual concentric conical array (DCCA) with uniform elements distribution and is used at the aircraft and HAP to achieve bidirectional beamforming. The antenna array elements are fed by an adaptiveexponent sine profile function to reduce the sidelobe levels while the low-profile dual conical array structure reduces the secondary major lobe and backlobe levels. The proposed beamforming technique is also capable of providing multibeam towards several aircrafts at the same time for effective resource sharing and management. The radiation performance of the array is demonstrated, analyzed, and compared with the concentric circular array where it is found that the secondary major lobe has been reduced by 13 dB with sidelobe level down to −40 dB relative to the mainlobe level. In addition, the bit energy-to-noise power spectral density and probability of bit error of the proposed aeronautical network has been investigated at different operating frequencies including 3.5 GHz and millimeter wave (mm-wave) frequencies of 28 and 39 GHz. The simulation results have shown that a channel capacity of about 3 Gbps can be achieved for BPSK and QPSK signals using bidirectional beamforming for a channel bandwidth of 400 MHz at 28 and 39 GHz mm-wave frequencies while it is about 773 Mbps at 3.5 GHz for 100 MHz bandwidth that can be provided over a line-of-sight distance of 896 km between an aircraft and HAP.