To identify non-protein coding as well as truncated or premature RNA sequences expressed and obtain more complete transcriptome information, we combined the MinION direct RNA-sequencing of a conventional poly(A) RNA purification method with poly(A)-tagging of the non-coding RNA (ncRNA) fraction. This approach was applied to transcriptome sequencing of the dicyemid mesozoan, Dicyema misakiense, which has minicircular mitochondrial DNA molecules where each molecule encodes a single gene, as well as the host. Using informatics analysis, we distinguished dicyemid RNAs from those of the host squid. The poly(A) RNAs were assigned to host mitochondrial genes, host nuclear protein-coding genes, Dicyema nuclear protein-coding genes, and Dicyema mitochondrial genes in the decreasing order. Our poly(A)-tailing method recovered significantly more ncRNAs from the host compared with the sequencing of poly(A) RNAs. Furthermore, our method captured various lengths of squid mitochondrial DNA (mtDNA) transcripts at different steps of maturation including a read of 3,500 bp, which covers 21% of the squid mitochondrial genome, possibly a premature host RNA product. In contrast, shorter and less abundant reads were recovered from the dicyemid mitochondrial RNAs (mtRNAs). Even the longest read was 307 bp covering only a part of a minicircle. This study revealed significantly different modes of the mitochondrial transcription between a mesozoan and the host. Our approach to perform direct RNA-sequencing combined with the poly(A)-tailing reaction can be an effective method to fully capture non-poly(A) transcripts in a wide range of organisms.