This paper presents a modular substrate-integrated waveguide (SIW) antenna array based on H-plane aperture structures for Ka-band. The unitary antenna is based on a SIW aperture antenna with an improved H-plane radiation pattern by means of the implementation of metallic vias in the wave propagation along the H-plane antenna. The inner metallic vias are introduced to form four different sub-apertures at the end of the H-plane aperture antenna, dividing the field from the feeding into four in-phase wavefronts. In that manner, a flatter wavefront is generated to achieve high directivity. Additionally, some periodic parallel strips are printed at the end of the antenna aperture to improve the impedance matching with the air. The Hplane antenna is used as the constituting element for an E-plane array antenna, using four H-plane elements. The E-plane array antenna increases the antenna directivity, providing a pencil-shape beam, based on a series coaxial feeding structure. This feeding strategy favours the antenna modularity at the expense of suffering from a slight beam steering with frequency in the working bandwidth. The proposed antenna has an impedance matching below-10 dB from 32.9 to 37.0 GHz (equivalent to 11.73% bandwidth) with a nearly stable gain of almost 10 dBi for the H-plane unitary element and 14 dBi for the E-plane array. Prototypes of both antennas are manufactured to validate the proposed unitary antenna and array designs.