要实现Android GridLayoutManager中一行只有一个背景图，可以通过自定义RecyclerView的ItemDecoration来实现。以下是示例代码：

1. 创建一个名为SingleBackgroundItemDecoration的自定义ItemDecoration类：

public class SingleBackgroundItemDecoration extends RecyclerView.ItemDecoration {
    private Drawable background;

    public SingleBackgroundItemDecoration(Context context, @DrawableRes int backgroundResId) {
        background = ContextCompat.getDrawable(context, backgroundResId);
    }

    @Override
    public void getItemOffsets(Rect outRect, View view, RecyclerView parent, RecyclerView.State state) {
        int position = parent.getChildAdapterPosition(view);
        int spanCount = ((GridLayoutManager) parent.getLayoutManager()).getSpanCount();
        if (position % spanCount == 0) {
            outRect.left = 0;
            outRect.right = parent.getWidth() - parent.getPaddingRight();
        } else {
            outRect.left = parent.getWidth();
            outRect.right = 0;
        }
    }

    @Override
    public void onDraw(Canvas c, RecyclerView parent, RecyclerView.State state) {
        int spanCount = ((GridLayoutManager) parent.getLayoutManager()).getSpanCount();
        int childCount = parent.getChildCount();
        for (int i = 0; i < childCount; i++) {
            View child = parent.getChildAt(i);
            int position = parent.getChildAdapterPosition(child);
            if (position % spanCount == 0) {
                background.setBounds(child.getLeft(), child.getTop(), child.getRight(), child.getBottom());
                background.draw(c);
            }
        }
    }
}

2. 在你的Activity或Fragment中，找到你的RecyclerView，并在设置LayoutManager后添加ItemDecoration：

RecyclerView recyclerView = findViewById(R.id.recycler_view);
recyclerView.setLayoutManager(new GridLayoutManager(this, spanCount));
recyclerView.addItemDecoration(new SingleBackgroundItemDecoration(this, R.drawable.background));

在这个示例中，我们假设你的背景图资源文件为background，你可以根据自己的需求修改背景图的资源和布局逻辑。