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This paper proposes an optically transparent series-fed microstrip array with small inter-element spacing and stepped feed lines for antenna-on-display applications. In the proposed series-fed array, the inconsistency of resonant frequencies between the input impedance at the edge of the feed line and the consecutive patch element produces multiple resonant frequencies. The small inter-element spacing in the array reduces input impedance variation among multiple resonant frequencies so that they are closely spaced, forming a broad impedance bandwidth. Also, stepped feed lines allow for impedance matching by a gradual decrease in characteristic impedance. Thus, impedance bandwidth and flat gain of the antenna are enhanced as the number of array elements increases. Optical transparency of the antenna is realized by using thin-metal meshes to be implemented on an active area of display panels. To validate the proposed approach, a $5 \times 1$ array antenna is fabricated and measured. The measured results exhibit a -10 dB impedance bandwidth of 14.2% ( $25.08-28.92$ GHz) and 3 dB gain bandwidth of 10.1% ( $26.2-29$ GHz) with 7.02 dBi peak gain at 27.4 GHz. Furthermore, the design is extended to a $5 \times 4$ array with a feeding network, demonstrating the beam scanning properties of ±20° and ±40° at 28 GHz with a bore-sight gain of 11.8 dBi.