Two-photon pumped upconversion intracavity lasing is achieved by placing a 1 cm-long dye-solution filled liquid cell inside a Q-switched Nd:YAG pulsed laser cavity. The upconversion gain medium is the solution of a new dye, trans-4-[p-(N-hydroxyethyl-N-methylamino)styryl]-N-methylpyridinium iodide, abbreviated as ASPI, which has strong two-photon absorption and subsequent upconversion fluorescence emission when excited with 1.06 mu m laser radiation. The spectral, temporal, and spatial properties of the upconverted cavity lasing output are investigated. The key parameters for upconversion lasing are emission wavelength of similar to 623 nm, pulse duration of similar to (2-10) ns, and beam divergence of similar to (2.5-4) mrad, The corresponding parameters for the pump lasing from the same cavity are similar to 1.06 mu m, similar to 20 ns, and similar to (5-7) mrad, respectively. The net conversion efficiency from the absorbed IR pump laser pulse energy to the visible lasing pulse energy is measured to be similar to 8.5%.