The famous neutron star Geminga was until quite lately the only pulsar undetected in the radio regime, though observed as a strong pulsating gamma- and X-ray source. Three independent groups from the Pushchino Radio Astronomy Observatory (Russia) reported recently the detection of pulsed radio emission from Geminga at 102.5 MHz, i.e., the first detection of the radio pulsar PSR J0633+1746 by Kuz'min & Losovskii, Malofeev & Malov and Shitov & Pugachev. This pulsar exhibits the weakest radio luminosity known. Its average pulse profile appears to be very wide, filling an entire 360 deg pulse window according to Kuz'min & Losovskii. We present a model explaining the peculiarities of the Geminga radio pulsar, based on the assumption that it is an almost aligned rotator. The electromagnetic waves generated in the inner magnetosphere reach the region within the light cylinder with a weak magnetic field (at distances of a few light cylinder radii), where they are strongly damped due to the cyclotron resonance with particles of magnetospheric electron-positron plasma. The lowest frequencies that can escape are determined by the value of the magnetic field in the region where the line of sight passes through the light cylinder. The specific viewing geometry of an almost aligned rotator implies that the observer's line of sight probes the emission region near the bundle of the last open field lines. This explains the unusually weak emission from Geminga's low-frequency radio pulsar.