This letter studies an open stopband elimination method for a class of periodic leaky-wave antenna (PLWA) composed of two varied uniform transmission lines in alternatively cascading arrangement. By using a transmission line model, a dispersion diagram is extracted and an equal phase shift condition of beta L-1(1) = beta L-2(2) is proposed to eliminate the open stopband at broad-side. The working principle is illustrated by numerical extraction and calculation. To verify the proposed method, an antenna prototype with two kinds of transmission lines-microstrip lines with and without covering strips-is accordingly designed and fabricated. Furthermore, simulated and measured results coincide well with the numerical prediction, showing that the proposed strip-covered uniform PLWA owns a certain radiation capability to continuously scan through the broadside direction.